<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>Int_Quotient_2</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Evaluate the following integral: \[ \int {@f@}d{@v@} \] [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Let \({@v@}+{@n1@}=R\), therefore \(d{@v@}=dR\)</p>
<p>\[\int{@f@}d{@v@} =\int\frac{@pR@}{R^2}dR\]</p>
<p>\[=\int\frac{@pRnext@}{R^2}dR=\int({@pRdivRsq@})dR\] \[={@correctanswerinR@}+c={@correctanswer@}\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020022400</text>
    </stackversion>
    <questionvariables>
      <text>n1:rand(3)+1;
n2:rand(2)+1;
  v:x;
  q:(v+n1)^2;
  p:v^3 + sum((-1)^n2*(rand(5)+1)*v^k,k,1,2)+(-1)^n2*(rand(5)+1);
  f:p/q;
  bcoeff:coeff(p,v,2);
  ccoeff:coeff(p,v,1);
  dcoeff:coeff(p,v,0);
  pR:ev((R-n1)^3 + bcoeff*(R-n1)^2+ccoeff*(R-n1)+dcoeff);
  pRnext:ev(expand((R-n1)^3) + expand(bcoeff*(R-n1)^2)+expand(ccoeff*(R-n1))+dcoeff);
  bRcoeff:coeff(pRnext,R,2);
  cRcoeff:coeff(pRnext,R,1);
  dRcoeff:coeff(pRnext,R,0);
  pRdivRsq:expand(pRnext/R^2);
  correctanswerinR:int(pRdivRsq,R);
  correctanswer:expand(int(f,v))+c;
  temp:expand(correctanswer);
  correctanswer2:(v+n1)^2/2 +bRcoeff*(v+n1) + cRcoeff*ln(|v+n1|) - dRcoeff/(v+n1)+c;
  wrongformanswer:(v+n1)^2/2 +bRcoeff*(v+n1) + cRcoeff*ln(v+n1) - dRcoeff/(v+n1)+c;
  wrongformanswer2:v^2/2 + (bRcoeff+n1)*v + cRcoeff*ln(v+n1) - dRcoeff/(v+n1)+c;</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\( \int {@f@} d{@v@} = {@correctanswer@} \)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <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>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>correctanswer</tans>
      <boxsize>20</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>integrate</forbidwords>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>Result</name>
      <value>2.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>Int</answertest>
        <sans>ans1</sans>
        <tans>correctanswer</tans>
        <testoptions> v</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-0-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>1</falsenextnode>
        <falseanswernote>Result-0-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>correctanswer2</tans>
        <testoptions>v</testoptions>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-1-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>2</falsenextnode>
        <falseanswernote>Result-1-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>diff(ans1,v)</sans>
        <tans>f</tans>
        <testoptions/>
        <quiet>1</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-2-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>Have you forgotten the constant of integration or is there an error in the integration of 1/f(x)?</p>]]></text>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>3</falsenextnode>
        <falseanswernote>Result-2-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>3</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>diff(f,v)</tans>
        <testoptions>v</testoptions>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-3-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>Result-3-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>2137065174</deployedseed>
    <deployedseed>2082151961</deployedseed>
    <deployedseed>1499532366</deployedseed>
    <deployedseed>907091122</deployedseed>
    <deployedseed>1576978666</deployedseed>
    <deployedseed>1176703572</deployedseed>
    <deployedseed>1338706886</deployedseed>
    <deployedseed>1325316518</deployedseed>
    <deployedseed>541891337</deployedseed>
    <deployedseed>6980862</deployedseed>
    <deployedseed>1752512931</deployedseed>
    <deployedseed>1894389032</deployedseed>
    <deployedseed>470932838</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>correctanswer</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>0</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-3-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>correctanswer2</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>4</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>wrongformanswer</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-2-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>5</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>wrongformanswer2</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-2-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>6</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>diff(f,v)</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-3-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>7</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>correctanswer-c</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-2-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
