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  • MathJax
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  • Integral Examples
Last edited by Volker Sorge 10 years ago
Page history

Integral Examples

Semantic Embedding Examples

(Outdated! Integrals have changed now!)

Integral Examples

Example 1

Original MathML:

<math>
  <mi>∫</mi>
  <mi>a</mi>
  <mo>+</mo>
  <mi>b</mi>
  <mi>dx</mi>
</math>

Semantic Tree:

<stree>
  <integral role="integral" id="6">
    <children>
      <largeop role="integral" id="0">∫</largeop>
      <infixop role="addition" id="5">
        +
        <content>
          <operator role="addition" id="2">+</operator>
        </content>
        <children>
          <identifier role="latinletter" font="italic" id="1">a</identifier>
          <identifier role="latinletter" font="italic" id="3">b</identifier>
        </children>
      </infixop>
      <identifier role="unknown" font="normal" id="4">dx</identifier>
    </children>
  </integral>
</stree>

Semantically enriched MathML:

<math type="integral" role="integral" id="6" children="0,5,4">
  <mi type="largeop" role="integral" id="0" parent="6">∫</mi>
  <mrow type="infixop" role="addition" id="5" children="1,3" content="2" parent="6">
    <mi type="identifier" role="latinletter" id="1" parent="5">a</mi>
    <mo type="operator" role="addition" id="2" operator="infixop,+" parent="5">+</mo>
    <mi type="identifier" role="latinletter" id="3" parent="5">b</mi>
  </mrow>
  <mi type="identifier" role="unknown" id="4" parent="6">dx</mi>
</math>

Example 2

Original MathML:

<math>
  <mi>∫</mi>
  <mi>∫</mi>
  <mi>∫</mi>
  <mi>dx</mi>
  <mi>dy</mi>
  <mi>dz</mi>
</math>

Semantic Tree:

<stree>
  <integral role="integral" id="9">
    <children>
      <largeop role="integral" id="0">∫</largeop>
      <integral role="integral" id="8">
        <children>
          <largeop role="integral" id="1">∫</largeop>
          <integral role="integral" id="7">
            <children>
              <largeop role="integral" id="2">∫</largeop>
              <empty role="unknown" id="6"/>
              <identifier role="unknown" font="normal" id="3">dx</identifier>
            </children>
          </integral>
          <identifier role="unknown" font="normal" id="4">dy</identifier>
        </children>
      </integral>
      <identifier role="unknown" font="normal" id="5">dz</identifier>
    </children>
  </integral>
</stree>

Semantically enriched MathML:

<math type="integral" role="integral" id="9" children="0,8,5">
  <mi type="largeop" role="integral" id="0" parent="9">∫</mi>
  <mrow type="integral" role="integral" id="8" children="1,7,4" parent="9">
    <mi type="largeop" role="integral" id="1" parent="8">∫</mi>
    <mrow type="integral" role="integral" id="7" children="2,6,3" parent="8">
      <mi type="largeop" role="integral" id="2" parent="7">∫</mi>
      <mrow type="empty" role="unknown" id="6" children="" parent="7"/>
      <mi type="identifier" role="unknown" id="3" parent="7">dx</mi>
    </mrow>
    <mi type="identifier" role="unknown" id="4" parent="8">dy</mi>
  </mrow>
  <mi type="identifier" role="unknown" id="5" parent="9">dz</mi>
</math>

Example 3

Original MathML:

<math>
  <munderover>
    <mi>∫</mi>
    <mn>0</mn>
    <mn>10</mn>
  </munderover>
  <mi>x</mi>
  <mi>dx</mi>
  <mo>+</mo>
  <munderover>
    <mi>∫</mi>
    <mn>10</mn>
    <mn>20</mn>
  </munderover>
  <mi>x</mi>
  <mi>dx</mi>
  <mo>=</mo>
  <munderover>
    <mi>∫</mi>
    <mn>0</mn>
    <mn>20</mn>
  </munderover>
  <mi>x</mi>
  <mi>dx</mi>
</math>

Semantic Tree:

<stree>
  <relseq role="equality" id="24">
    =
    <content>
      <relation role="equality" id="13">=</relation>
    </content>
    <children>
      <infixop role="addition" id="23">
        +
        <content>
          <operator role="addition" id="6">+</operator>
        </content>
        <children>
          <integral role="integral" id="22">
            <children>
              <limboth role="integral" id="3">
                <children>
                  <largeop role="integral" id="0">∫</largeop>
                  <number role="integer" font="normal" id="1">0</number>
                  <number role="integer" font="normal" id="2">10</number>
                </children>
              </limboth>
              <identifier role="latinletter" font="italic" id="4">x</identifier>
              <identifier role="unknown" font="normal" id="5">dx</identifier>
            </children>
          </integral>
          <integral role="integral" id="21">
            <children>
              <limboth role="integral" id="10">
                <children>
                  <largeop role="integral" id="7">∫</largeop>
                  <number role="integer" font="normal" id="8">10</number>
                  <number role="integer" font="normal" id="9">20</number>
                </children>
              </limboth>
              <identifier role="latinletter" font="italic" id="11">x</identifier>
              <identifier role="unknown" font="normal" id="12">dx</identifier>
            </children>
          </integral>
        </children>
      </infixop>
      <integral role="integral" id="20">
        <children>
          <limboth role="integral" id="17">
            <children>
              <largeop role="integral" id="14">∫</largeop>
              <number role="integer" font="normal" id="15">0</number>
              <number role="integer" font="normal" id="16">20</number>
            </children>
          </limboth>
          <identifier role="latinletter" font="italic" id="18">x</identifier>
          <identifier role="unknown" font="normal" id="19">dx</identifier>
        </children>
      </integral>
    </children>
  </relseq>
</stree>

Semantically enriched MathML:

<math type="relseq" role="equality" id="24" children="23,20" content="13">
  <mrow type="infixop" role="addition" id="23" children="22,21" content="6" parent="24">
    <mrow type="integral" role="integral" id="22" children="3,4,5" parent="23">
      <munderover type="limboth" role="integral" id="3" children="0,1,2" parent="22">
        <mi type="largeop" role="integral" id="0" parent="3">∫</mi>
        <mn type="number" role="integer" id="1" parent="3">0</mn>
        <mn type="number" role="integer" id="2" parent="3">10</mn>
      </munderover>
      <mi type="identifier" role="latinletter" id="4" parent="22">x</mi>
      <mi type="identifier" role="unknown" id="5" parent="22">dx</mi>
    </mrow>
    <mo type="operator" role="addition" id="6" operator="infixop,+" parent="23">+</mo>
    <mrow type="integral" role="integral" id="21" children="10,11,12" parent="23">
      <munderover type="limboth" role="integral" id="10" children="7,8,9" parent="21">
        <mi type="largeop" role="integral" id="7" parent="10">∫</mi>
        <mn type="number" role="integer" id="8" parent="10">10</mn>
        <mn type="number" role="integer" id="9" parent="10">20</mn>
      </munderover>
      <mi type="identifier" role="latinletter" id="11" parent="21">x</mi>
      <mi type="identifier" role="unknown" id="12" parent="21">dx</mi>
    </mrow>
  </mrow>
  <mo type="relation" role="equality" id="13" operator="relseq,=" parent="24">=</mo>
  <mrow type="integral" role="integral" id="20" children="17,18,19" parent="24">
    <munderover type="limboth" role="integral" id="17" children="14,15,16" parent="20">
      <mi type="largeop" role="integral" id="14" parent="17">∫</mi>
      <mn type="number" role="integer" id="15" parent="17">0</mn>
      <mn type="number" role="integer" id="16" parent="17">20</mn>
    </munderover>
    <mi type="identifier" role="latinletter" id="18" parent="20">x</mi>
    <mi type="identifier" role="unknown" id="19" parent="20">dx</mi>
  </mrow>
</math>
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