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<quiz>
<!-- question: 17332  -->
  <question type="stack">
    <name>
      <text>Integration</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<br>
<div class="stack-comment">
<h2>Practice of methods and feedback</h2>
<p>This symbolic integration question is typical of many mathematical methods. </p>
<p>In this case get the question <em>wrong</em>.  E.g. by typing in something like <span style="font-family: 'courier new', courier, monospace; color: #0000ff;">(3*x^2+1)^3+c</span> as an answer.</p>
<p>Feedback is given to students which includes a calculation of the student's answer.  This is designed to help students check their own work, and hence improve on this task. </p>
</div>
<br>
<p>Find \[ \int {@p@} d{@v@}\] [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We can either do this question by inspection (i.e. spot the answer) or in a more formal manner by using the substitution \[ u = ({@v@}-{@a@}).\] Then, since \(\frac{d}{d{@v@}}u=1\) we have \[ \int {@p@} d{@v@} = \int u^{@n@} du = \frac{u^{@n+1@}}{@n+1@}+c = {@ta@}+c.\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber></idnumber>
    <stackversion>
      <text>2025030700</text>
    </stackversion>
    <questionvariables>
      <text>n:rand(5)+3;
 a:rand(5)+3;
 v:x
 p:(v-a)^n;
 ta:(v-a)^(n+1)/(n+1);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(\int {@p@} d{@v@} = {@ta@}+c\)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text></text>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta+c</tans>
      <boxsize>20</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>int</forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
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      <name>prt1</name>
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        <text></text>
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        <name>0</name>
        <description></description>
        <answertest>Int</answertest>
        <sans>ans1</sans>
        <tans>ta</tans>
        <testoptions>v</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>1-0-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>1-0-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
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    <qtest>
      <testcase>1</testcase>
      <description></description>
      <testinput>
        <name>ans1</name>
        <value>ta+c</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>1-0-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description></description>
      <testinput>
        <name>ans1</name>
        <value>ta</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>1-0-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description></description>
      <testinput>
        <name>ans1</name>
        <value>ev(n*(v-a)^(n-1),simp)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>1-0-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>4</testcase>
      <description></description>
      <testinput>
        <name>ans1</name>
        <value>(v-a)^(n+1)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>1-0-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>5</testcase>
      <description></description>
      <testinput>
        <name>ans1</name>
        <value>ev(float(ta),simp)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore></expectedscore>
        <expectedpenalty></expectedpenalty>
        <expectedanswernote>NULL</expectedanswernote>
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    </qtest>
  </question>

</quiz>