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<quiz>
  <question type="stack">
    <name>
      <text>14.4.2.3 Exercise 2</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p> Find the area of the surface generated when \(y ={@y@}\) in the interval \({@a@}\leq x \leq {@b@}\) is rotated about the \(x\)-axis. Give your answer in <b>exact</b> form.</p>
<p>The area is [[input:ans1]]</p>
<p>[[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Given \(y ={@y@}\) then \( \dfrac{\mathrm{d}y}{\mathrm{d}y}= \displaystyle {@dy@}.\)</p>
<p>Using the formula \[\text{area}=\int_a^b 2\pi y \sqrt{1+\left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^2} \ \mathrm{d}x,\] the area of the surface generated is calculated to be: \[A = \int_{{@a@}}^{{@b@}} 2\pi ({@y@}) \sqrt{1+{@dy^2@}} \ \mathrm{d}x = \left[ {@I@} \right]_{{@a@}}^{{@b@}}= {@ta1@}.\]</p>]]></text>
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    <stackversion>
      <text>2021071900</text>
    </stackversion>
    <questionvariables>
      <text>/* I created a list of values for [m,a,b] which give reasonable values of the integral*/
VL: rand([[1,1,2], [1,1,6], [2,1,2], [2,1,5], [2,1,8], [2,1,11], [1,2,6], [1,2,12], [2,2,3], [2,2,5], [2,2,8]])

m: VL[1];
y: m*sqrt(x);

a: VL[2];   /*lower limit*/
b: VL[3];   /*upper limit */

dy: diff(y, x);
I: integrate(2*pi*y*sqrt(1+(dy)^2), x);
I2: expand(I)
ta1: integrate(2*pi*y*sqrt(1+(dy)^2), x, 0, b);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(y ={@y@}\) interval \({@a@}\leq x \leq {@b@}, \, A={@ta1@}\)</text>
    </questionnote>
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      <text/>
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    <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> Your answer is partially correct.</span>]]></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>
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        <name>ans1</name>
        <value>ta1</value>
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        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
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      <testcase>2</testcase>
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        <name>ans1</name>
        <value>ev(ta1+1,simp)</value>
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