<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>CR-Int-11-linearity-2.a</text>
    </name>
    <questiontext format="html">
      <text>Integrate {@p@} with respect to {@v@}.

[[input:ans1]] [[validation:ans1]]</text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[To solve this problem we will have to use the linearity rules for integration <hint>calc_int_linearity_rule</hint> as follows:

\[\begin{array}{rcl}\displaystyle 
 \int [{@p@}] d{@v@} &\displaystyle =&\displaystyle  \int {@pp1@} d{@v@} + \int {@pp2@} d{@v@} \\
   &\displaystyle =&\displaystyle  {@rdm1@}\int {@ppp1@} d{@v@} + \int {@ppp2@} d{@v@} \\
   &\displaystyle =&\displaystyle  {@rdm1@}\left[{@int(ppp1,v)@}\right] + \left[{@int(ppp2,v)@}\right] + c \\
   &\displaystyle =&\displaystyle  {@int(p,v)@} + c
 \end{array}\]]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>v:x;
rdm1:2+rand(4);
rdm2:2+rand(4);
ppp1:v;
ppp2:cos(rdm2*v);
pp1:rdm1*ppp1;
pp2:ppp2;
p:pp1+pp2;</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[\int {@p@} d{@v@} = {@int(p,v)@}+c\]</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>int(p,v)+c</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>Result</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text>q:ppp1+ppp2;</text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>Int</answertest>
        <sans>ans1</sans>
        <tans>int(p,v)+c</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>1</falsenextnode>
        <falseanswernote>Result-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>diff(ans1,v)</sans>
        <tans>-p</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-2-T</trueanswernote>
        <truefeedback format="html">
          <text>Your answer is the negative of the expected result. Have you checked your signs?</text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>2</falsenextnode>
        <falseanswernote>Result-2-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>diff(ans1,v)</sans>
        <tans>q</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-3-T</trueanswernote>
        <truefeedback format="html">
          <text>You appear to have used {@q@} as the integrand and forgotten the constant coefficient {@rdm1@}.</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>743989876</deployedseed>
    <deployedseed>661535593</deployedseed>
    <deployedseed>986753401</deployedseed>
    <deployedseed>954005029</deployedseed>
    <deployedseed>1941226561</deployedseed>
    <deployedseed>1854530594</deployedseed>
    <deployedseed>1451019942</deployedseed>
    <deployedseed>1077947613</deployedseed>
    <deployedseed>1701483422</deployedseed>
    <deployedseed>880491148</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(int(p,v)+c,simp)</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(int(p,v),simp)</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>Result-3-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
