qu.1.topic=Arclength@

qu.1.1.mode=Multiple Choice@
qu.1.1.name=ArcLength@
qu.1.1.comment=<p>The arclength of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>f</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math>&nbsp;from <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>a</mi></mrow></mstyle></math>&nbsp;to <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>b</mi></mrow></mstyle></math>is given by</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></munderover><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>y</mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mstyle></math></p>@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$a=rint(1,5);
$b=rint($a+1,3*$a);
$z=rint(5);
$f=switch($z,"$a*x^(2/3)","x^2/2+ln(x)/4","ln(x)","$a*sqrt(x)","cosh(x)");
$fp="diff($f,x)";
$E1="sqrt(1+factor(($fp)^2))";
$E2="sqrt(1+factor(($f)^2))";
$E3="sqrt(1+1/($fp)^2)";
$E4="sqrt(1+1/($f)^2)";
$E5="1-factor(($fp)^2)";
$M=maple(" 
MathML[ExportPresentation]($f),
MathML[ExportPresentation]($E1),
MathML[ExportPresentation]($E2),
MathML[ExportPresentation]($E3),
MathML[ExportPresentation]($E4),
MathML[ExportPresentation]($E5)
");

$display=switch(0,$M);
$displayE1=switch(1,$M);
$displayE2=switch(2,$M);
$displayE3=switch(3,$M);
$displayE4=switch(4,$M);
$displayE5=switch(5,$M);
$pa=plotmaple("plot($f,x=-1..$b,thickness=2,tickmarks=[2,2
]),plotdevice='gif', plotoptions='height=350,width=350'");@
qu.1.1.uid=00ca75a9-e8dc-48a3-ae63-c0b133ad05ce@
qu.1.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Arclength;
  Sub-Topic=Setup;
@
qu.1.1.question=<p>Which of the following gives the arc length from <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$a</mi></mrow></mstyle></math> to <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$b</mi></mrow></mstyle></math> of the curve <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math>$display?</p>
<p>$pa</p>@
qu.1.1.answer=1@
qu.1.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mi    mathvariant='normal' >$a</mi><mi    mathvariant='normal' >$b</mi></munderover><mrow></mrow></mrow><mrow><mo    mathvariant='normal'             >&InvisibleTimes;</mo></mrow></mrow></math>$displayE1<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>dx</mi></mrow></mstyle></math>@
qu.1.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mi    mathvariant='normal' >$a</mi><mi    mathvariant='normal' >$b</mi></munderover><mrow></mrow></mrow><mrow><mo    mathvariant='normal'             >&InvisibleTimes;</mo></mrow></mrow></math>$displayE2<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>dx</mi></mrow></mstyle></math>@
qu.1.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mi    mathvariant='normal' >$a</mi><mi    mathvariant='normal' >$b</mi></munderover><mrow></mrow></mrow><mrow><mo    mathvariant='normal'             >&InvisibleTimes;</mo></mrow></mrow></math>$displayE3<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>dx</mi></mrow></mstyle></math>@
qu.1.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mi    mathvariant='normal' >$a</mi><mi    mathvariant='normal' >$b</mi></munderover><mrow></mrow></mrow><mrow><mo    mathvariant='normal'             >&InvisibleTimes;</mo></mrow></mrow></math>$displayE4<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>dx</mi></mrow></mstyle></math>@
qu.1.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mi    mathvariant='normal' >$a</mi><mi    mathvariant='normal' >$b</mi></munderover><mrow></mrow></mrow><mrow><mo    mathvariant='normal'             >&InvisibleTimes;</mo></mrow></mrow></math>$displayE5<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>dx</mi></mrow></mstyle></math>@
qu.1.1.fixed=@

qu.1.2.mode=Multiple Choice@
qu.1.2.name=Circumference@
qu.1.2.comment=<p>How would you modify this integral so that you would find the length of the upper half of the ellipse <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup><mrow><msup><mi>a</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><msup><mi>y</mi><mrow><mn>2</mn></mrow></msup><mrow><msup><mi>b</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow></mstyle></math>?</p>@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$r=rint(2,7);
$R=$r^2;
$tr=2*$r;
$pa=plotmaple("plot([$r*cos(t),$r*sin(t),t=0..Pi],x=-$r..$r,y=-$r..$r,thickness=2,tickmarks=[2,2
]),plotdevice='gif', plotoptions='height=250,width=250'");@
qu.1.2.uid=b8cb3c25-ace6-45a3-b954-753e2e1b5a44@
qu.1.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Arclength;
  Sub-Topic=Setup;
@
qu.1.2.question=<p>$pa</p>
<p>Which of the following integrals gives the length of a semicircle of radius <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$r</mi></mrow></mstyle></math>?</p>@
qu.1.2.answer=1@
qu.1.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$r</mi><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$r</mi></mrow><mi    mathvariant='normal' >$r</mi></munderover></mrow><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mrow><mrow><msqrt><mrow><mrow><mi    mathvariant='normal' >$R</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow></mrow></msqrt></mrow></mrow></mfrac><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&InvisibleTimes;</mo><mi    mathvariant='italic' >dx</mi></mrow></mrow></math>@
qu.1.2.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$r</mi></mrow><mi    mathvariant='normal' >$r</mi></munderover></mrow><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$tr</mi></mrow><mrow><mrow><msqrt><mrow><mrow><mrow><mrow><mi    mathvariant='normal' >$R</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow></mrow></mrow></mrow></msqrt></mrow></mrow></mfrac><mi    mathvariant='italic' >dx</mi></mrow></mrow></math>@
qu.1.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$r</mi></mrow><mi    mathvariant='normal' >$r</mi></munderover></mrow><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mrow><mrow><msqrt><mrow><mrow><mrow><mi    mathvariant='normal' >$R</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow></mrow></mrow></msqrt></mrow></mrow></mfrac><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&InvisibleTimes;</mo><mi    mathvariant='italic' >dx</mi></mrow></mrow></math>@
qu.1.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$r</mi></mrow><mi    mathvariant='normal' >$r</mi></munderover></mrow><mrow><mrow><msqrt><mrow><mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><mrow><msup ><mfenced><mrow><mi    mathvariant='normal' >$R</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&InvisibleTimes;</mo></mrow></mrow></mrow></msqrt></mrow><mi    mathvariant='italic' >dx</mi></mrow></mrow></math>@
qu.1.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='italic' >&pi;</mi></mrow><mrow><munderover  accentunder='false'><mo    mathvariant='normal'  form='prefix' fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='true' symmetric='unset' maxsize='' minsize='' largeop='true' movablelimits='unset' accent='unset'>&Integral;</mo><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$r</mi></mrow><mi    mathvariant='normal' >$r</mi></munderover></mrow><mrow><mrow><msqrt><mrow><mrow><mrow><mrow><mi    mathvariant='normal' >$R</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&InvisibleTimes;</mo></mrow></mrow></mrow></mrow></msqrt></mrow><mi    mathvariant='italic' >dx</mi></mrow></mrow></math>@
qu.1.2.fixed=@

qu.1.3.question=<p>$pa</p>
<p>Find the arc length from <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow></mstyle></math> to <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$a</mi></mrow></mstyle></math> of the curve given by $display. Give your answer to TWO decimal places. <br />
<br />
(HINTS: The integral you will have to evaluate is NOT HARD. To get your approximation, work out your answer exactly using THE Fundamental Theorem of Calculus--F(b)-F(a)--and then go to Maple and use "evalf(F(b)-F(a))".)<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.1.3.maple=evalb(abs(evalf($ANSWER)-evalf($RESPONSE))<.01);@
qu.1.3.allow2d=0@
qu.1.3.maple_answer=evalf(int($E,x=1..$a),5)@
qu.1.3.type=maple@
qu.1.3.mode=Maple@
qu.1.3.name=computeArcLength@
qu.1.3.comment=<p>Arclength <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><munderover><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></munderover><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>y</mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow><mrow><mi></mi></mrow><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow></mrow></mstyle></math></p>@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$a=rint(2,5);
$z=rint(6);
$f=switch($z, "$a*x^(2/3)", "x^2/2-ln(x)/4",
"2*(x+$a)^(3/2)-2*(1+$a)^(3/2)","2/3*(x^2-1)^(3/2)","cosh(x)","x^3/6+1/(2*x)");
$fp="diff($f,x)";
$display=maple("printf(MathML[ExportPresentation](y=$f))");
$E="sqrt(1+factor(($fp)^2))";
$pa=plotmaple("plot($f,x=0..2*$a,view=[-1..2*$a,-1..5],thickness=2,tickmarks=[2,2
]),plotdevice='gif', plotoptions='height=350,width=350'");@
qu.1.3.uid=0e9cd018-738a-4d96-bb44-57f66c81982f@
qu.1.3.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Medium;
  Course=Introduction to Calculus II;
  Topic=Arclength;
  Sub-Topic=Compute;
@

