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Formula trapezelor </text> </region> <region region-id="748" left="12" top="47.25" width="77.25" height="22.5" align-x="35.25" align-y="66" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="749" left="12" top="87" width="24" height="12.75" align-x="23.25" align-y="96" show-border="false" 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is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> vectorii <sp/> xi - captele subintervalelor echidistante </text> </region> <region region-id="774" left="210" top="152.25" width="113.25" height="24" align-x="227.25" align-y="162" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> integrala definita pe [a,b] cu metoda trapezelor </text> </region> <region region-id="758" left="18" top="145.5" width="174.75" height="43.5" align-x="51.75" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="trapez">I</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id 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xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.12973820125274657</ml:real> </result> </ml:eval> </math> <rendering item-idref="14"/> </region> <region region-id="766" left="258" top="272.25" width="151.5" height="12" align-x="275.25" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> integrala cu operatorul de integrare </text> </region> <region region-id="767" left="18" top="303" width="145.5" height="22.5" align-x="88.5" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="def">I</ml:id> <ml:id xml:space="preserve" subscript="trapez">I</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.0031995555438281975</ml:real> </result> </ml:eval> </math> <rendering item-idref="15"/> </region> <region region-id="768" left="204" top="422.25" width="204.75" height="12" align-x="204.75" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> t = x - momentul zilei la care s-a facut mas/ora </text> </region> <region region-id="769" left="24" top="344.25" width="39.75" height="194.25" align-x="33.75" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">t</ml:id> <ml:matrix rows="12" cols="1"> <ml:real>13</ml:real> <ml:real>14</ml:real> <ml:real>15</ml:real> <ml:real>16</ml:real> <ml:real>17</ml:real> <ml:real>18</ml:real> <ml:real>19</ml:real> <ml:real>20</ml:real> <ml:real>21</ml:real> <ml:real>22</ml:real> <ml:real>23</ml:real> <ml:real>24</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="770" left="126" top="344.25" width="48.75" height="194.25" align-x="138" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P</ml:id> <ml:matrix rows="12" cols="1"> <ml:real>4.03</ml:real> <ml:real>3.83</ml:real> <ml:real>3.86</ml:real> <ml:real>3.95</ml:real> <ml:real>4.20</ml:real> <ml:real>4.46</ml:real> <ml:real>4.67</ml:real> <ml:real>4.98</ml:real> <ml:real>4.84</ml:real> <ml:real>4.42</ml:real> <ml:real>3.29</ml:real> <ml:real>2.64</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="771" left="204" top="440.25" width="230.25" height="12" align-x="206.25" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> P = y - puterea activa consumata la fiecare mom/ora </text> </region> <region region-id="772" left="204" top="458.25" width="48.75" height="12" align-x="206.25" align-y="468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> E - energia </text> </region> <region region-id="776" left="204" top="481.5" width="70.5" height="39" align-x="216.75" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="true"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>13</ml:real> <ml:real>24</ml:real> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="777" left="24" top="549" width="28.5" height="12.75" align-x="35.25" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:real>13</ml:real> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="778" left="84" top="549" width="30" height="12.75" align-x="96.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:real>24</ml:real> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="779" left="144" top="549" width="31.5" height="12.75" align-x="158.25" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:real>11</ml:real> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="780" left="204" top="542.25" width="46.5" height="27.75" align-x="216.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="791" left="276" top="555" width="29.25" height="12.75" align-x="287.25" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="23"/> </region> <region region-id="781" left="24" top="571.5" width="135.75" height="43.5" align-x="36.75" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="782" left="180" top="585" width="49.5" height="12.75" align-x="191.25" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>45.835</ml:real> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="783" left="234" top="584.25" width="29.25" height="12" align-x="240" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> [kW/h] </text> </region> <region region-id="784" left="18" top="638.25" width="210.75" height="12" align-x="29.25" align-y="648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> putem folosi o functie de interpolare, parabolica: </text> </region> <region region-id="785" left="24" top="657" width="74.25" height="12.75" align-x="39.75" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">M</ml:id> <ml:apply> <ml:id xml:space="preserve">pspline</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">P</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="786" left="24" top="675" width="96.75" height="12.75" align-x="47.25" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">interp</ml:id> <ml:sequence> <ml:id xml:space="preserve">M</ml:id> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="787" left="24" top="691.5" width="68.25" height="39" align-x="36.75" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">F</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>13</ml:real> <ml:real>24</ml:real> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="788" left="144" top="705" width="58.5" height="12.75" align-x="155.25" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>45.825822744411063</ml:real> </result> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="789" left="18" top="728.25" width="377.25" height="36" align-x="44.25" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Imbunatatirea preciziei: 1) interval mai mare, cu un numar mare de puncte intermediare ---> precizie mai buna 2) aplicarea unei formule cu o precizie mai buna ==> SIMPSON </text> </region> <region region-id="790" left="18" top="770.25" width="101.25" height="12" align-x="21" align-y="780" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 2. Formula lui Simpson </text> </region> <region region-id="792" left="24" top="797.25" width="77.25" height="22.5" align-x="47.25" align-y="816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="793" left="18" top="831" width="24" height="12.75" align-x="29.25" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="794" left="66" top="831" width="25.5" height="12.75" align-x="78.75" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:real>7</ml:real> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="795" left="120" top="831" width="31.5" height="12.75" align-x="134.25" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:real>10</ml:real> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="796" left="204" top="824.25" width="46.5" height="27.75" align-x="216.75" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="797" left="282" top="831" width="36" height="12.75" align-x="293.25" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.3</ml:real> </result> </ml:eval> </math> <rendering item-idref="35"/> </region> <region region-id="798" left="18" top="861" width="48" height="18" align-x="30.75" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="799" left="120" top="861" width="48.75" height="18" align-x="132.75" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="800" left="198" top="861" width="71.25" height="12.75" align-x="208.5" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:sequence> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="801" left="312" top="861" width="72.75" height="12.75" align-x="324" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="802" left="18" top="878.25" width="233.25" height="36.75" align-x="62.25" align-y="894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="Simpson">I</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">h</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="803" left="282" top="891" width="85.5" height="16.5" align-x="324.75" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="Simpson">I</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.12953556413971737</ml:real> </result> </ml:eval> </math> <rendering item-idref="41"/> </region> <region region-id="804" left="24" top="914.25" width="201" height="24" align-x="24" align-y="924" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> integrala definita pe [a,b] cu metoda trapezelor </text> </region> <region region-id="805" left="24" top="931.5" width="75" height="39" align-x="48" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="def">I</ml:id> <ml:apply> <ml:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:real>7</ml:real> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="806" left="132" top="945" width="65.25" height="16.5" align-x="154.5" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="def">I</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.12973820125274657</ml:real> </result> </ml:eval> </math> <rendering item-idref="43"/> </region> <region region-id="807" left="24" top="969" width="156" height="22.5" align-x="105" align-y="984" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="def">I</ml:id> <ml:id xml:space="preserve" subscript="Simpson">I</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.00020263711302920262</ml:real> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="808" left="12" top="1010.25" width="203.25" height="12" align-x="31.5" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 3. Integrarea dubla </text> </region> <region region-id="809" left="18" top="1035" width="131.25" height="18.75" align-x="51" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:absval/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>-3</ml:real> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="810" left="18" top="1065" width="24" height="12.75" align-x="29.25" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="811" left="72" top="1065" width="25.5" height="12.75" align-x="84.75" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:real>5</ml:real> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="812" left="132" top="1065" width="29.25" height="12.75" align-x="143.25" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> <ml:real>-2</ml:real> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="813" left="186" top="1065" width="25.5" height="12.75" align-x="198.75" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">d</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="814" left="252" top="1059" width="39.75" height="18.75" align-x="270" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Nx</ml:id> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="815" left="318" top="1059" width="41.25" height="18.75" align-x="337.5" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Ny</ml:id> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="816" left="18" top="1088.25" width="49.5" height="27.75" align-x="33.75" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Nx</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="817" left="90" top="1088.25" width="51" height="27.75" align-x="107.25" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="y">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">d</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="818" left="162" top="1095" width="48" height="16.5" align-x="176.25" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.025</ml:real> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> <region region-id="819" left="228" top="1095" width="45" height="16.5" align-x="243.75" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="y">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.03</ml:real> </result> </ml:eval> </math> <rendering item-idref="55"/> </region> <region region-id="820" left="282" top="1094.25" width="75" height="12" align-x="291" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> pasii de integrare </text> </region> <region region-id="821" left="18" top="1125" width="48" height="12.75" align-x="27" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Nx</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="56"/> </region> <region region-id="822" left="96" top="1125" width="51" height="12.75" align-x="106.5" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="823" left="174" top="1125" width="51.75" height="18" align-x="186.75" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve" subscript="x">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="58"/> </region> <region region-id="824" left="264" top="1125" width="57" height="18" align-x="279" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve" subscript="y">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="826" left="12" top="1148.25" width="119.25" height="12" align-x="14.25" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> I. Integram dupa variabila y </text> </region> <region region-id="827" left="18" top="1173" width="78" height="12.75" align-x="30" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="60"/> </region> <region region-id="828" left="120" top="1173" width="75.75" height="12.75" align-x="129.75" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">l</ml:id> <ml:range> <ml:sequence> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="829" left="18" top="1186.5" width="295.5" height="40.5" align-x="33.75" align-y="1206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="x">I</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="y">h</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">l</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="830" left="6" top="1226.25" width="163.5" height="12" align-x="9.75" align-y="1236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> II. Integram dupa x, folosind Simpson </text> </region> <region region-id="831" left="18" top="1239" width="76.5" height="12.75" align-x="30" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Nx</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="63"/> </region> <region region-id="832" left="126" top="1239" width="74.25" height="12.75" align-x="135.75" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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<compatibility multiple-assignment="MC12" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="834" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="746" left="6" top="14.25" width="369" height="12" align-x="14.25" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="11"> !!! LAB 8 SOPORAN ELENA-ADRIANA 1621/3 29.11.2017 !!! </f> </text> </region> <region region-id="747" left="6" top="32.25" width="93.75" height="12" align-x="22.5" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 1. Formula trapezelor </text> </region> <region region-id="748" left="12" top="47.25" width="77.25" height="22.5" align-x="35.25" align-y="66" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="749" left="12" top="87" width="24" height="12.75" align-x="23.25" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="750" left="60" top="87" width="25.5" height="12.75" align-x="72.75" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:real>7</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="751" left="114" top="87" width="31.5" height="12.75" align-x="128.25" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:real>20</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="752" left="180" top="80.25" width="46.5" height="27.75" align-x="192.75" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="753" left="252" top="87" width="36" height="12.75" align-x="263.25" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.3</ml:real> </result> </ml:eval> </math> <rendering item-idref="6"/> </region> <region region-id="754" left="294" top="86.25" width="135.75" height="12" align-x="300" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> (N - pct intermediare de calcul) </text> </region> <region region-id="755" left="18" top="117" width="36.75" height="12.75" align-x="27" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> 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is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> vectorii <sp/> xi - captele subintervalelor echidistante </text> </region> <region region-id="774" left="210" top="152.25" width="113.25" height="24" align-x="227.25" align-y="162" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> integrala definita pe [a,b] cu metoda trapezelor </text> </region> <region region-id="758" left="18" top="145.5" width="174.75" height="43.5" align-x="51.75" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="trapez">I</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id 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align-x="374.25" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="trapez">I</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.13293775679657477</ml:real> </result> </ml:eval> </math> <rendering item-idref="10"/> </region> <region region-id="761" left="24" top="206.25" width="303.75" height="27.75" align-x="40.5" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Er</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:real>24</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="762" left="24" top="237" width="95.25" height="18.75" align-x="39" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Er</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.0036846276755689803</ml:real> </result> </ml:eval> </math> <rendering item-idref="12"/> </region> <region region-id="763" left="144" top="242.25" width="70.5" height="12" align-x="159" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> eroarea metodei </text> </region> <region region-id="764" left="18" top="254.25" width="104.25" height="44.25" align-x="42" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="def">I</ml:id> <ml:apply> <ml:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:real>7</ml:real> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="765" left="168" top="273" width="65.25" height="16.5" align-x="190.5" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="def">I</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.12973820125274657</ml:real> </result> </ml:eval> </math> <rendering item-idref="14"/> </region> <region region-id="766" left="258" top="272.25" width="151.5" height="12" align-x="275.25" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> integrala cu operatorul de integrare </text> </region> <region region-id="767" left="18" top="303" width="145.5" height="22.5" align-x="88.5" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="def">I</ml:id> <ml:id xml:space="preserve" subscript="trapez">I</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.0031995555438281975</ml:real> </result> </ml:eval> </math> <rendering item-idref="15"/> </region> <region region-id="768" left="204" top="422.25" width="204.75" height="12" align-x="204.75" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> t = x - momentul zilei la care s-a facut mas/ora </text> </region> <region region-id="769" left="24" top="344.25" width="39.75" height="194.25" align-x="33.75" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">t</ml:id> <ml:matrix rows="12" cols="1"> <ml:real>13</ml:real> <ml:real>14</ml:real> <ml:real>15</ml:real> <ml:real>16</ml:real> <ml:real>17</ml:real> <ml:real>18</ml:real> <ml:real>19</ml:real> <ml:real>20</ml:real> <ml:real>21</ml:real> <ml:real>22</ml:real> <ml:real>23</ml:real> <ml:real>24</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="770" left="126" top="344.25" width="48.75" height="194.25" align-x="138" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P</ml:id> <ml:matrix rows="12" cols="1"> <ml:real>4.03</ml:real> <ml:real>3.83</ml:real> <ml:real>3.86</ml:real> <ml:real>3.95</ml:real> <ml:real>4.20</ml:real> <ml:real>4.46</ml:real> <ml:real>4.67</ml:real> <ml:real>4.98</ml:real> <ml:real>4.84</ml:real> <ml:real>4.42</ml:real> <ml:real>3.29</ml:real> <ml:real>2.64</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="771" left="204" top="440.25" width="230.25" height="12" align-x="206.25" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> P = y - puterea activa consumata la fiecare mom/ora </text> </region> <region region-id="772" left="204" top="458.25" width="48.75" height="12" align-x="206.25" align-y="468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> E - energia </text> </region> <region region-id="776" left="204" top="481.5" width="70.5" height="39" align-x="216.75" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="true"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>13</ml:real> <ml:real>24</ml:real> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="777" left="24" top="549" width="28.5" height="12.75" align-x="35.25" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:real>13</ml:real> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="778" left="84" top="549" width="30" height="12.75" align-x="96.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:real>24</ml:real> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="779" left="144" top="549" width="31.5" height="12.75" align-x="158.25" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:real>11</ml:real> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="780" left="204" top="542.25" width="46.5" height="27.75" align-x="216.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="791" left="276" top="555" width="29.25" height="12.75" align-x="287.25" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="23"/> </region> <region region-id="781" left="24" top="571.5" width="135.75" height="43.5" align-x="36.75" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="782" left="180" top="585" width="49.5" height="12.75" align-x="191.25" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>45.835</ml:real> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="783" left="234" top="584.25" width="29.25" height="12" align-x="240" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> [kW/h] </text> </region> <region region-id="784" left="18" top="638.25" width="210.75" height="12" align-x="29.25" align-y="648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> putem folosi o functie de interpolare, parabolica: </text> </region> <region region-id="785" left="24" top="657" width="74.25" height="12.75" align-x="39.75" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">M</ml:id> <ml:apply> <ml:id xml:space="preserve">pspline</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">P</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="786" left="24" top="675" width="96.75" height="12.75" align-x="47.25" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">interp</ml:id> <ml:sequence> <ml:id xml:space="preserve">M</ml:id> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="787" left="24" top="691.5" width="68.25" height="39" align-x="36.75" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">F</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>13</ml:real> <ml:real>24</ml:real> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="788" left="144" top="705" width="58.5" height="12.75" align-x="155.25" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>45.825822744411063</ml:real> </result> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="789" left="18" top="728.25" width="377.25" height="36" align-x="44.25" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Imbunatatirea preciziei: 1) interval mai mare, cu un numar mare de puncte intermediare ---> precizie mai buna 2) aplicarea unei formule cu o precizie mai buna ==> SIMPSON </text> </region> <region region-id="790" left="18" top="770.25" width="101.25" height="12" align-x="21" align-y="780" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 2. Formula lui Simpson </text> </region> <region region-id="792" left="24" top="797.25" width="77.25" height="22.5" align-x="47.25" align-y="816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="793" left="18" top="831" width="24" height="12.75" align-x="29.25" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="794" left="66" top="831" width="25.5" height="12.75" align-x="78.75" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:real>7</ml:real> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="795" left="120" top="831" width="31.5" height="12.75" align-x="134.25" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:real>10</ml:real> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="796" left="204" top="824.25" width="46.5" height="27.75" align-x="216.75" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="797" left="282" top="831" width="36" height="12.75" align-x="293.25" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.3</ml:real> </result> </ml:eval> </math> <rendering item-idref="35"/> </region> <region region-id="798" left="18" top="861" width="48" height="18" align-x="30.75" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="799" left="120" top="861" width="48.75" height="18" align-x="132.75" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="800" left="198" top="861" width="71.25" height="12.75" align-x="208.5" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:sequence> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="801" left="312" top="861" width="72.75" height="12.75" align-x="324" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="802" left="18" top="878.25" width="233.25" height="36.75" align-x="62.25" align-y="894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="Simpson">I</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">h</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="803" left="282" top="891" width="85.5" height="16.5" align-x="324.75" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="Simpson">I</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.12953556413971737</ml:real> </result> </ml:eval> </math> <rendering item-idref="41"/> </region> <region region-id="804" left="24" top="914.25" width="201" height="24" align-x="24" align-y="924" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> integrala definita pe [a,b] cu metoda trapezelor </text> </region> <region region-id="805" left="24" top="931.5" width="75" height="39" align-x="48" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="def">I</ml:id> <ml:apply> <ml:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:real>7</ml:real> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="806" left="132" top="945" width="65.25" height="16.5" align-x="154.5" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="def">I</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.12973820125274657</ml:real> </result> </ml:eval> </math> <rendering item-idref="43"/> </region> <region region-id="807" left="24" top="969" width="156" height="22.5" align-x="105" align-y="984" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="def">I</ml:id> <ml:id xml:space="preserve" subscript="Simpson">I</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.00020263711302920262</ml:real> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="808" left="12" top="1010.25" width="203.25" height="12" align-x="31.5" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 3. Integrarea dubla </text> </region> <region region-id="809" left="18" top="1035" width="131.25" height="18.75" align-x="51" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:absval/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>-3</ml:real> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="810" left="18" top="1065" width="24" height="12.75" align-x="29.25" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="811" left="72" top="1065" width="25.5" height="12.75" align-x="84.75" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:real>5</ml:real> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="812" left="132" top="1065" width="29.25" height="12.75" align-x="143.25" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> <ml:real>-2</ml:real> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="813" left="186" top="1065" width="25.5" height="12.75" align-x="198.75" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">d</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="814" left="252" top="1059" width="39.75" height="18.75" align-x="270" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Nx</ml:id> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="815" left="318" top="1059" width="41.25" height="18.75" align-x="337.5" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Ny</ml:id> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="816" left="18" top="1088.25" width="49.5" height="27.75" align-x="33.75" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Nx</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="817" left="90" top="1088.25" width="51" height="27.75" align-x="107.25" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="y">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">d</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="818" left="162" top="1095" width="48" height="16.5" align-x="176.25" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.025</ml:real> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> <region region-id="819" left="228" top="1095" width="45" height="16.5" align-x="243.75" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="y">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.03</ml:real> </result> </ml:eval> </math> <rendering item-idref="55"/> </region> <region region-id="820" left="282" top="1094.25" width="75" height="12" align-x="291" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> pasii de integrare </text> </region> <region region-id="821" left="18" top="1125" width="48" height="12.75" align-x="27" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Nx</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="56"/> </region> <region region-id="822" left="96" top="1125" width="51" height="12.75" align-x="106.5" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="823" left="174" top="1125" width="51.75" height="18" align-x="186.75" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve" subscript="x">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="58"/> </region> <region region-id="824" left="264" top="1125" width="57" height="18" align-x="279" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve" subscript="y">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="826" left="12" top="1148.25" width="119.25" height="12" align-x="14.25" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> I. Integram dupa variabila y </text> </region> <region region-id="827" left="18" top="1173" width="78" height="12.75" align-x="30" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="60"/> </region> <region region-id="828" left="120" top="1173" width="75.75" height="12.75" align-x="129.75" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">l</ml:id> <ml:range> <ml:sequence> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="829" left="18" top="1186.5" width="295.5" height="40.5" align-x="33.75" align-y="1206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="x">I</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="y">h</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Ny</ml:id> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">l</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="830" left="6" top="1226.25" width="163.5" height="12" align-x="9.75" align-y="1236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> II. Integram dupa x, folosind Simpson </text> </region> <region region-id="831" left="18" top="1239" width="76.5" height="12.75" align-x="30" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">Nx</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="63"/> </region> <region region-id="832" left="126" top="1239" width="74.25" height="12.75" align-x="135.75" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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