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  <settings>
    <identity>
      <id>be8ed228-7b9f-4d88-9521-f6039e697cd5</id>
      <revision>56</revision>
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    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
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    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
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      <assembly name="MaximaPlugin" version="1.0.5048.41981" guid="44011c1e-5d0d-4533-8e68-e32b5badce41" />
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  </settings>
  <region id="0" left="18" top="18" width="226" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Integrale mit Maßeinheiten</p>
    </text>
    <text lang="eng">
      <p bold="true">Integrals with units</p>
    </text>
  </region>
  <region id="1" left="504" top="18" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Chapter Units.sm">Maßeinheiten</p>
    </text>
    <text lang="eng">
      <p href="Chapter Units.sm">Units of Measurement</p>
    </text>
  </region>
  <region id="2" left="504" top="36" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section Math Integrals.sm">Integrale</p>
    </text>
    <text lang="eng">
      <p href="Section Math Integrals.sm">Integrals</p>
    </text>
  </region>
  <region id="3" left="504" top="54" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
  </region>
  <region id="4" left="504" top="72" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
  </region>
  <region id="5" left="18" top="108" width="587" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Mit dem Maxima-Plugin kann SMath Integrale mit Maßeinheiten berechnen.</p>
    </text>
    <text lang="eng">
      <p>With Maxima plugin, the function int() can handle integrals with units.</p>
    </text>
  </region>
  <region id="6" left="18" top="144" width="625" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" style="string">takeover</e>
        <e type="function" preserve="true" args="1">MaximaControl</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">int(), diff(), sum() and lim() now use Maxima</e>
      </result>
    </math>
  </region>
  <region id="7" left="153" top="180" width="86" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">q.0</e>
        <e type="operand">10</e>
        <e type="operand" style="unit">N</e>
        <e type="operand" style="unit">mm</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="8" left="18" top="189" width="108" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">q</e>
        <e type="operand">q.0</e>
        <e type="operand">m</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="9" left="288" top="189" width="398" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Funktion q(x) erwartet ein Argument der 
Dimension Länge und liefert Werte der Dimension
Kraft pro Länge. </p>
    </text>
    <text lang="eng">
      <p>The function q(x) expects the argument to be of
dimension length and returns values of dimension
force per length.</p>
    </text>
  </region>
  <region id="10" left="18" top="216" width="98" height="50" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">m</e>
        <e type="operand">0.2</e>
        <e type="operand" style="unit">N</e>
        <e type="operand" style="unit">mm</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="11" left="135" top="216" width="118" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="function" args="1">q</e>
      </input>
      <contract>
        <e type="operand" style="unit">N</e>
        <e type="operand" style="unit">mm</e>
        <e type="operator" args="2">/</e>
      </contract>
      <result action="numeric">
        <e type="operand">410</e>
      </result>
    </math>
  </region>
  <region id="12" left="288" top="261" width="438" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Funktion soll im Bereich von 1 bis 3m integriert
werden.</p>
    </text>
    <text lang="eng">
      <p>The function is to be integrated over the interval
from 1 to 3m.</p>
    </text>
  </region>
  <region id="13" left="18" top="279" width="66" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.1</e>
        <e type="operand">1</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="14" left="99" top="279" width="66" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.2</e>
        <e type="operand">3</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="15" left="18" top="315" width="240" height="118" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="0.00974168134603182" scale_y="2.99914616204689" scale_z="0.00974168134603182" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-89" transpose_y="-37" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="function" args="1">q</e>
        <e type="operand" style="unit">N</e>
        <e type="operand" style="unit">mm</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">/</e>
        <e type="operand">x</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x.1</e>
        <e type="operator" args="2">&gt;</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x.2</e>
        <e type="operator" args="2">&lt;</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
      </input>
    </plot>
  </region>
  <region id="16" left="288" top="315" width="403" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Für die Darstellung muss die Funktion durch die 
Ergebniseinheit geteilt werden und x mit der
erwarteten Einheit des Funktionsarguments 
multipliziert werden.</p>
    </text>
    <text lang="eng">
      <p>The plot function provides unit-less x values and
expects unit-less expression values. Therefore the
x is multiplied by m and the result is divided
by N/mm</p>
    </text>
  </region>
  <region id="17" left="288" top="387" width="146" height="82" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">q</e>
        <e type="operand">x</e>
        <e type="operand">x.1</e>
        <e type="operand">x.2</e>
        <e type="function" preserve="true" args="4">int</e>
      </input>
      <contract>
        <e type="operand" style="unit">kN</e>
      </contract>
      <result action="symbolic">
        <e type="operand">820</e>
      </result>
    </math>
  </region>
  <region id="18" top="486" color="#000000" bgColor="#ffffff">
    <area collapsed="false">
      <title lang="ger">
        <p>Alternativen</p>
      </title>
      <title lang="eng">
        <p>Alternatives</p>
      </title>
    </area>
    <region id="19" left="18" top="504" width="151" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p underline="true">SMath ohne Maxima</p>
      </text>
      <text lang="eng">
        <p underline="true">SMath without Maxima</p>
      </text>
    </region>
    <region id="20" left="18" top="540" width="684" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand" style="string">surrender</e>
          <e type="function" preserve="true" args="1">MaximaControl</e>
        </input>
        <result action="numeric">
          <e type="operand" style="string">int(), diff(), sum() and lim() now are native SMath</e>
        </result>
      </math>
    </region>
    <region id="21" left="18" top="576" width="298" height="82" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
          <e type="function" args="1">q</e>
          <e type="operand">x</e>
          <e type="operand">x.1</e>
          <e type="operand">x.2</e>
          <e type="function" preserve="true" args="4">int</e>
        </input>
        <result action="symbolic">
          <e type="operand">10000</e>
          <e type="operand" style="unit">kg</e>
          <e type="operator" args="2">*</e>
          <e type="operand" style="unit">m</e>
          <e type="operand">20</e>
          <e type="operand">x</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand" style="unit">m</e>
          <e type="operand" style="unit">s</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">x</e>
          <e type="operand" style="unit">m</e>
          <e type="operand">3</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
          <e type="function" preserve="true" args="4">int</e>
        </result>
      </math>
    </region>
    <region id="22" left="315" top="576" width="415" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Die Integration mit int() scheitert, weil die
Maßeinheiten der Integrationsgrenzen ignoriert
werden und die Integrationsvariable dimensionslos
ist. </p>
      </text>
      <text lang="eng">
        <p>Integration with int() fails, because the units of 
the limits are ignored and the function is called 
with a unit-less argument instead of a length value.</p>
      </text>
    </region>
    <region id="23" left="18" top="675" width="300" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p underline="true">Benutzung des Plugins Maple Wrapper</p>
      </text>
      <text lang="eng">
        <p underline="true">Option 1: Use Maple Wrapper plugin</p>
      </text>
    </region>
    <region id="24" left="18" top="702" width="199" height="84" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
          <e type="function" args="1">q</e>
          <e type="operand">x</e>
          <e type="operand">x.1</e>
          <e type="operand">x.2</e>
          <e type="function" preserve="true" args="4">int</e>
          <e type="function" preserve="true" args="1">maple</e>
        </input>
        <contract>
          <e type="operand" style="unit">kN</e>
        </contract>
        <result action="symbolic">
          <e type="operand">820</e>
        </result>
      </math>
    </region>
    <region id="25" left="288" top="702" width="411" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Die Funktion maple() aus dem Plugin MapleWrapper 
kommt mit Maßeinheiten zurecht.</p>
      </text>
      <text lang="eng">
        <p>The function maple() can handle units in integrals.</p>
      </text>
    </region>
    <region id="26" left="288" top="747" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p href="maple.sm">maple()</p>
      </text>
    </region>
    <region id="27" left="18" top="783" width="456" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p underline="true">Transformation auf dimensionslose Integrationsvariable</p>
      </text>
      <text lang="eng">
        <p underline="true">Option 2: Transform the integration variable</p>
      </text>
    </region>
    <region id="28" left="18" top="819" width="129" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand" preserve="false" style="unit">LE</e>
          <e type="operand">x.2</e>
          <e type="operand">x.1</e>
          <e type="operator" args="2">-</e>
          <e type="function" preserve="true" args="1">UoM</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="29" left="288" top="819" width="407" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Das Integral kann mit Hilfe der Maßeinheiten der
Integrationsgrenzen in dimensionslose Form über-
führt werden. </p>
      </text>
      <text lang="eng">
        <p>The integration variable can be made unit-less using
the units of the integration limits.</p>
      </text>
    </region>
    <region id="30" left="18" top="846" width="198" height="116" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand" preserve="false" style="unit">LE</e>
          <e type="operand">x</e>
          <e type="operand" preserve="false" style="unit">LE</e>
          <e type="operator" args="2">*</e>
          <e type="function" args="1">q</e>
          <e type="operand">x</e>
          <e type="operand">x.1</e>
          <e type="operand" preserve="false" style="unit">LE</e>
          <e type="operator" args="2">/</e>
          <e type="operand">x.2</e>
          <e type="operand" preserve="false" style="unit">LE</e>
          <e type="operator" args="2">/</e>
          <e type="function" preserve="true" args="4">int</e>
          <e type="operator" args="2">*</e>
        </input>
        <contract>
          <e type="operand" style="unit">kN</e>
        </contract>
        <result action="numeric">
          <e type="operand">820</e>
        </result>
      </math>
    </region>
    <region id="31" left="288" top="882" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p href="UoM.sm">UoM()</p>
      </text>
    </region>
    <region id="32" left="18" top="963" width="578" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p underline="true">So könnte eine einheitensichere Integrationsfunktion definiert werden</p>
      </text>
      <text lang="eng">
        <p underline="true">This could be a function for unit-proof integration</p>
      </text>
    </region>
    <region id="33" left="27" top="999" width="471" height="204" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f#</e>
          <e type="operand">x#</e>
          <e type="operand">a#</e>
          <e type="operand">b#</e>
          <e type="function" args="4">Int</e>
          <e type="operand">u#</e>
          <e type="operand">b#</e>
          <e type="operand">a#</e>
          <e type="operator" args="2">-</e>
          <e type="function" preserve="true" args="1">UoM</e>
          <e type="operator" args="2">:</e>
          <e type="operand">sf#</e>
          <e type="operand">f#</e>
          <e type="function" preserve="true" args="1">num2str</e>
          <e type="operator" args="2">:</e>
          <e type="operand">sx#</e>
          <e type="operand">x#</e>
          <e type="function" preserve="true" args="1">num2str</e>
          <e type="operator" args="2">:</e>
          <e type="operand">sxu#</e>
          <e type="operand">x#</e>
          <e type="operand">u#</e>
          <e type="operator" args="2">*</e>
          <e type="function" preserve="true" args="1">num2str</e>
          <e type="operator" args="2">:</e>
          <e type="operand">ft#</e>
          <e type="operand">sf#</e>
          <e type="operand">sx#</e>
          <e type="operand">sxu#</e>
          <e type="function" preserve="true" args="3">strrep</e>
          <e type="function" preserve="true" args="1">str2num</e>
          <e type="operator" args="2">:</e>
          <e type="operand">u#</e>
          <e type="operand">ft#</e>
          <e type="operand">x#</e>
          <e type="operand">a#</e>
          <e type="operand">u#</e>
          <e type="operator" args="2">/</e>
          <e type="operand">b#</e>
          <e type="operand">u#</e>
          <e type="operator" args="2">/</e>
          <e type="function" preserve="true" args="4">int</e>
          <e type="operator" args="2">*</e>
          <e type="operand">6</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="8">line</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="34" left="513" top="1008" width="199" height="104" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Hier wird die Variable
x# im Ausdruck f# durch
das Produkt von x# mal 
der Maßeinheit der 
Intervallbreite b#-a#
ersetzt.</p>
      </text>
      <text lang="eng">
        <p>Here, the variable x# in
expression f# is replaced
by the product of x# times
the unit of the intervall
size b#-a#</p>
      </text>
    </region>
    <region id="35" left="36" top="1206" width="227" height="35" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
          <e type="function" args="1">q</e>
          <e type="operand">x</e>
          <e type="operand">x.1</e>
          <e type="operand">x.2</e>
          <e type="function" args="4">Int</e>
        </input>
        <contract>
          <e type="operand" style="unit">kN</e>
        </contract>
        <result action="numeric">
          <e type="operand">820</e>
        </result>
      </math>
    </region>
    <region id="36" left="36" top="1233" width="248" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand" style="unit">g</e>
          <e type="operand">t</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
          <e type="function" args="4">Int</e>
        </input>
        <result action="numeric">
          <e type="operand">4.9033</e>
          <e type="operand" style="unit">m</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="37" top="1269" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="38" left="18" top="1305" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Chapter Units.sm">Maßeinheiten</p>
    </text>
    <text lang="eng">
      <p href="Chapter Units.sm">Units of Measurement</p>
    </text>
  </region>
  <region id="39" left="18" top="1323" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section Math Integrals.sm">Integrale</p>
    </text>
    <text lang="eng">
      <p href="Section Math Integrals.sm">Integrals</p>
    </text>
  </region>
  <region id="40" left="18" top="1341" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
  </region>
  <region id="41" left="18" top="1359" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
  </region>
  <region id="42" left="18" top="1395" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-11-10 18:06:03 +0100 (So, 10. Nov 2013) $ </p>
    </text>
  </region>
</regions>