qu.1.topic=1-computing sums@

qu.1.1.question=Compute 
<math>
  <munderover>
    <mo mathsize="150%">&sum;</mo>
    <mrow>
      <mi>i</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mrow>
      <mi>$n</mi>
    </mrow>
  </munderover>
  <mo>(</mo>
  <mi>$a</mi>
  <mo>&InvisibleTimes;</mo>
  <mi>i</mi>
  <mo>+</mo>
  <mi>$b</mi>
  <mo>)</mo>
</math>.@
qu.1.1.answer.num=$answer@
qu.1.1.answer.units=@
qu.1.1.showUnits=false@
qu.1.1.grading=exact_value@
qu.1.1.negStyle=minus@
qu.1.1.numStyle=thousands   @
qu.1.1.mode=Numeric@
qu.1.1.comment=The answer is $answer.@
qu.1.1.editing=useHTML@
qu.1.1.algorithm=$n=range(30,60,10);
$a=range(2,5);
$b=range(2,9);
$answer=$b*$n+$a*$n*($n+1)/2;@

qu.1.2.mode=Inline@
qu.1.2.editing=useHTML@
qu.1.2.algorithm=$b=range(2,9);
$dx=switch(rint(4),0.1,0.2,0.4,0.5);
$xa=$dx;
$xb=2*$dx;
$xc=3*$dx;
$xd=4*$dx;
$fa=$dx^2+$b*$dx;
$fb=4*$dx^2+2*$b*$dx;
$fc=9*$dx^2+3*$b*$dx;
$fd=16*$dx^2+4*$b*$dx;
$answer=(30*$dx^2+10*$b*$dx)*$dx;@
qu.1.2.weighting=1,1,1@
qu.1.2.numbering=alpha@
qu.1.2.part.1.editing=useHTML@
qu.1.2.part.1.question=(Unset)@
qu.1.2.part.1.answer=$xa, $xb, $xc, $xd@
qu.1.2.part.1.mode=Ntuple@
qu.1.2.part.2.editing=useHTML@
qu.1.2.part.2.question=(Unset)@
qu.1.2.part.2.answer=$fa, $fb, $fc, $fd@
qu.1.2.part.2.mode=Ntuple@
qu.1.2.part.3.answer.units=@
qu.1.2.part.3.numStyle=   @
qu.1.2.part.3.editing=useHTML@
qu.1.2.part.3.showUnits=false@
qu.1.2.part.3.question=(Unset)@
qu.1.2.part.3.mode=Numeric@
qu.1.2.part.3.grading=exact_value@
qu.1.2.part.3.negStyle=minus@
qu.1.2.part.3.answer.num=$answer@
qu.1.2.question=Let 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
  <mo>=</mo>
  <msup>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>2</mn>
    </mrow>
  </msup>
  <mo>+</mo>
  <mi>$b</mi>
  <mo>&InvisibleTimes;</mo>
  <mi>x</mi>
</math>, 
set 
<math>
  <mi>&Delta;</mi>
  <mo>&InvisibleTimes;</mo>
  <mi>x</mi>
  <mo>=</mo>
  <mi>$dx</mi>
</math>, 
and let 
<math>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
  <mo>=</mo>
  <mi>i</mi>
  <mo>&InvisibleTimes;</mo>
  <mi>&Delta;</mi>
  <mo>&InvisibleTimes;</mo>
  <mi>x</mi>
</math>.
<br>
<br>
Enter 
<math>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>1</mn>
    </mrow>
  </msub>
</math>, 
<math>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>2</mn>
    </mrow>
  </msub>
</math>, 
<math>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>3</mn>
    </mrow>
  </msub>
</math>, 
<math>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>4</mn>
    </mrow>
  </msub>
</math>, 
separated by commas.
<br>
<1> &#160;
<br>
<br>
Enter 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>1</mn>
    </mrow>
  </msub>
  <mo>)</mo>
</math>, 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>2</mn>
    </mrow>
  </msub>
  <mo>)</mo>
</math>,
<math>
  <mi>f</mi>
  <mo>(</mo>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>3</mn>
    </mrow>
  </msub>
  <mo>)</mo>
</math>, 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>4</mn>
    </mrow>
  </msub>
  <mo>)</mo>
</math>, 
separated by commas.
<br>
<2> &#160;
<br>
<br>
Compute 
<math>
  <munderover>
  <mo mathsize="150%">&sum;</mo>
    <mrow>
      <mi>i</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mrow>
      <mn>4</mn>
    </mrow>
  </munderover>
  <mrow>
    <mi>f</mi>
    <mo>(</mo>
    <msub>
      <mrow>
        <mi>x</mi>
      </mrow>
      <mrow>
        <mi>i</mi>
      </mrow>
    </msub>
    <mo>)</mo>
    <mtext>&ThinSpace;</mtext>
    <mi>&Delta;</mi>
    <mo>&InvisibleTimes;</mo>
    <mi>x</mi>
  </mrow>
</math>.
<br>
<3> &#160;@



qu.2.topic=2-Riemann sums@

qu.2.1.mode=Inline@
qu.2.1.editing=useHTML@
qu.2.1.algorithm=$a=range(1,3);
$n=range(2,3);
$c=range(2,9);
$dx=switch(rint(2),0.2,0.4);
$b=$a+4*$dx;
$xa=$a+$dx;
$xb=$a+2*$dx;
$xc=$a+3*$dx;
$xd=$a+4*$dx;
$fa=10*$xa^$n+$c;
$fb=10*$xb^$n+$c;
$fc=10*$xc^$n+$c;
$fd=10*$xd^$n+$c;
$answer=($fa+$fb+$fc+$fd)*$dx;@
qu.2.1.weighting=1,1,1@
qu.2.1.numbering=alpha@
qu.2.1.part.1.editing=useHTML@
qu.2.1.part.1.question=(Unset)@
qu.2.1.part.1.answer=$xa, $xb, $xc, $xd@
qu.2.1.part.1.mode=Ntuple@
qu.2.1.part.2.editing=useHTML@
qu.2.1.part.2.question=(Unset)@
qu.2.1.part.2.answer=$fa, $fb, $fc, $fd@
qu.2.1.part.2.mode=Ntuple@
qu.2.1.part.3.answer.units=@
qu.2.1.part.3.numStyle=   @
qu.2.1.part.3.editing=useHTML@
qu.2.1.part.3.showUnits=false@
qu.2.1.part.3.question=(Unset)@
qu.2.1.part.3.mode=Numeric@
qu.2.1.part.3.grading=exact_value@
qu.2.1.part.3.negStyle=minus@
qu.2.1.part.3.answer.num=$answer@
qu.2.1.question=Let &#160; 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
  <mo>=</mo>
  <mn>10</mn>
  <mo>&InvisibleTimes;</mo>
  <msup>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>$n</mi>
    </mrow>
  </msup>
  <mo>+</mo>
  <mi>$c</mi>
</math>.
<br>
List the evaluation points 
<math>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
</math> 
needed in a 
<strong>right-hand</strong> 
Riemann sum on the interval 
<math>
  <mo>[</mo>
  <mi>$a</mi>
  <mo>,</mo>
  <mi>$b</mi>
  <mo>]</mo>
</math>,
<br>
using <math><mn>4</mn></math> points.  Separate your answers with commas.
<br>
<br>
<1> &#160;
<br>
<br>
List the values 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
  <mo>)</mo>
</math>, 
separated by commas. Use the exact values.
<br>
<2> &#160;
<br>
<br>
Compute the Riemann sum. Use the exact value.
<br>
<3> &#160;@

qu.2.2.mode=Inline@
qu.2.2.editing=useHTML@
qu.2.2.algorithm=$a=range(1,3);
$n=range(2,3);
$c=range(2,9);
$dx=switch(rint(2),0.2,0.4);
$b=$a+4*$dx;
$xa=$a;
$xb=$a+$dx;
$xc=$a+2*$dx;
$xd=$a+3*$dx;
$fa=10*$xa^$n+$c;
$fb=10*$xb^$n+$c;
$fc=10*$xc^$n+$c;
$fd=10*$xd^$n+$c;
$answer=($fa+$fb+$fc+$fd)*$dx;@
qu.2.2.weighting=1,1,1@
qu.2.2.numbering=alpha@
qu.2.2.part.1.editing=useHTML@
qu.2.2.part.1.question=(Unset)@
qu.2.2.part.1.answer=$xa, $xb, $xc, $xd@
qu.2.2.part.1.mode=Ntuple@
qu.2.2.part.2.editing=useHTML@
qu.2.2.part.2.question=(Unset)@
qu.2.2.part.2.answer=$fa, $fb, $fc, $fd@
qu.2.2.part.2.mode=Ntuple@
qu.2.2.part.3.answer.units=@
qu.2.2.part.3.numStyle=   @
qu.2.2.part.3.editing=useHTML@
qu.2.2.part.3.showUnits=false@
qu.2.2.part.3.question=(Unset)@
qu.2.2.part.3.mode=Numeric@
qu.2.2.part.3.grading=exact_value@
qu.2.2.part.3.negStyle=minus@
qu.2.2.part.3.answer.num=$answer@
qu.2.2.question=Let &#160; 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
  <mo>=</mo>
  <mn>10</mn>
  <mo>&InvisibleTimes;</mo>
  <msup>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>$n</mi>
    </mrow>
  </msup>
  <mo>+</mo>
  <mi>$c</mi>
</math>.
<br>
List the evaluation points 
<math>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
</math>
needed in a 
<strong>left-hand</strong>
Riemann sum on the interval 
<math>
  <mo>[</mo>
  <mi>$a</mi>
  <mo>,</mo>
  <mi>$b</mi>
  <mo>]</mo>
</math>,
<br>
using <math><mn>4</mn></math> points.  Separate your answers with commas.
<br>
<br>
<1> &#160;
<br>
<br>
List the values 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
  <mo>)</mo>
</math>, 
separated by commas. Use the exact values.
<br>
<2> &#160;
<br>
<br>
Compute the Riemann sum. Use the exact value.
<br>
<3> &#160;@

qu.2.3.mode=Inline@
qu.2.3.editing=useHTML@
qu.2.3.algorithm=$a=range(1,3);
$n=2;
$c=range(2,9);
$dx=switch(rint(2),0.2,0.4);
$b=$a+4*$dx;
$xa=$a+.5*$dx;
$xb=$a+1.5*$dx;
$xc=$a+2.5*$dx;
$xd=$a+3.5*$dx;
$fa=10*$xa^$n+$c;
$fb=10*$xb^$n+$c;
$fc=10*$xc^$n+$c;
$fd=10*$xd^$n+$c;
$answer=($fa+$fb+$fc+$fd)*$dx;@
qu.2.3.weighting=1,1,1@
qu.2.3.numbering=alpha@
qu.2.3.part.1.editing=useHTML@
qu.2.3.part.1.question=(Unset)@
qu.2.3.part.1.answer=$xa, $xb, $xc, $xd@
qu.2.3.part.1.mode=Ntuple@
qu.2.3.part.2.editing=useHTML@
qu.2.3.part.2.question=(Unset)@
qu.2.3.part.2.answer=$fa, $fb, $fc, $fd@
qu.2.3.part.2.mode=Ntuple@
qu.2.3.part.3.answer.units=@
qu.2.3.part.3.numStyle=   @
qu.2.3.part.3.editing=useHTML@
qu.2.3.part.3.showUnits=false@
qu.2.3.part.3.question=(Unset)@
qu.2.3.part.3.mode=Numeric@
qu.2.3.part.3.grading=exact_value@
qu.2.3.part.3.negStyle=minus@
qu.2.3.part.3.answer.num=$answer@
qu.2.3.question=Let &#160; 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <mi>x</mi>
  <mo>)</mo>
  <mo>=</mo>
  <mn>10</mn>
  <mo>&InvisibleTimes;</mo>
  <msup>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>$n</mi>
    </mrow>
  </msup>
  <mo>+</mo>
  <mi>$c</mi>
</math>.
<br>
List the evaluation points 
<math>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
</math>
needed in a 
<strong>midpoint</strong> 
Riemann sum on the interval 
<math>
  <mo>[</mo>
  <mi>$a</mi>
  <mo>,</mo>
  <mi>$b</mi>
  <mo>]</mo>
</math>,
<br>
using <math><mn>4</mn></math> points.  Separate your answers with commas.
<br>
<br>
<1> &#160;
<br>
<br>
List the values 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
  <mo>)</mo>
</math>, 
separated by commas. Use the exact values.
<br>
<2> &#160;
<br>
<br>
Compute the Riemann sum. Use the exact value.
<br>
<3> &#160;@



qu.3.topic=3-exact computation of quadratic integrals@

qu.3.1.mode=Inline@
qu.3.1.editing=useHTML@
qu.3.1.algorithm=$a=range(1,10);
$c=2*$a;
$b=range(2,5);
$F=mathml(3*x^2+2*$a*x);
$dx=$b/n;
$xi=$b*i/n;
$fi=(3*$b^2/n^2)*i^2+(2*$a*$b/n)*i;
$fidx=(3*$b^3/n^3)*i^2+(2*$a*$b^2/n^2)*i;
$rsum=$b^3*(n+1)*(2*n+1)/(2*n^2)+$a*$b^2*(n+1)/n;
$integral=$b^3+$a*$b^2;@
qu.3.1.weighting=1,1,1,1,1,1@
qu.3.1.numbering=alpha@
qu.3.1.part.1.editing=useHTML@
qu.3.1.part.1.question=(Unset)@
qu.3.1.part.1.answer=$dx@
qu.3.1.part.1.mode=Formula@
qu.3.1.part.2.editing=useHTML@
qu.3.1.part.2.question=(Unset)@
qu.3.1.part.2.answer=$xi@
qu.3.1.part.2.mode=Formula@
qu.3.1.part.3.editing=useHTML@
qu.3.1.part.3.question=(Unset)@
qu.3.1.part.3.answer=$fi@
qu.3.1.part.3.mode=Formula@
qu.3.1.part.4.editing=useHTML@
qu.3.1.part.4.question=(Unset)@
qu.3.1.part.4.answer=$fidx@
qu.3.1.part.4.mode=Formula@
qu.3.1.part.5.editing=useHTML@
qu.3.1.part.5.question=(Unset)@
qu.3.1.part.5.answer=$rsum@
qu.3.1.part.5.mode=Formula@
qu.3.1.part.6.answer.units=@
qu.3.1.part.6.numStyle=thousands   @
qu.3.1.part.6.editing=useHTML@
qu.3.1.part.6.showUnits=false@
qu.3.1.part.6.question=(Unset)@
qu.3.1.part.6.mode=Numeric@
qu.3.1.part.6.grading=exact_value@
qu.3.1.part.6.negStyle=minus@
qu.3.1.part.6.answer.num=$integral@
qu.3.1.question=Consider the 
<strong>right-hand</strong> Riemann sum representing the area under the graph of 
<br>
$F from <math><mn>0</mn></math> to <math><mn>$b</mn></math> using <math><mi>n</mi></math> 
equal subdivisions.
<br>
<br>
What is <math><mi>&Delta;x</mi></math>?  
(Your answer should be a function of <math><mi>n</mi></math>.)
<br>
<1> &#160;
<br>
<br>
What is the general formula for 
<math>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
</math>
for the Riemann sum in terms of 
<math><mi>n</mi></math>?
<br>
<2> &#160;
<br>
<br>
What is the general formula for 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
  <mo>)</mo>
</math>
in terms of 
<math><mi>n</mi></math>?
<br>
<3> &#160;
<br>
<br>
What is the general formula for 
<math>
  <mi>f</mi>
  <mo>(</mo>
  <msub>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mi>i</mi>
    </mrow>
  </msub>
  <mo>)</mo>
  <mtext>&ThinSpace;</mtext>
  <mi>&Delta;x</mi>
</math>
in terms of 
<math><mi>n</mi></math>?
<br>
<4> &#160;
<br>
<br>
Use the formulas 
<math>
  <munderover>
    <mo>&sum;</mo>
    <mrow>
      <mi>i</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mrow>
      <mi>n</mi>
    </mrow>
  </munderover>
  <mi>i</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>n</mi>
      <mo>(</mo>
      <mi>n</mi>
      <mo>+</mo>
      <mn>1</mn>
      <mo>)</mo>
    </mrow>
    <mrow>
      <mn>2</mn>
    </mrow>
  </mfrac>
</math> 
and 
<math>
  <munderover>
    <mo>&sum;</mo>
    <mrow>
      <mi>i</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mrow>
      <mi>n</mi>
    </mrow>
  </munderover>
  <msup>
    <mrow>
      <mi>i</mi>
    </mrow>
    <mrow>
      <mn>2</mn>
    </mrow>
  </msup>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>n</mi>
      <mo>(</mo>
      <mi>n</mi>
      <mo>+</mo>
      <mn>1</mn>
      <mo>)</mo>
      <mo>(</mo>
      <mn>2</mn>
      <mi>n</mi>
      <mo>+</mo>
      <mn>1</mn>
      <mo>)</mo>
    </mrow>
    <mrow>
      <mn>6</mn>
    </mrow>
  </mfrac>
</math>
<br>
to compute the Riemann sum in terms of 
<math><mi>n</mi></math>.
<br>
<5> &#160;
<br>
<br>
Compute 
<math>
  <msubsup>
    <mrow>
      <mo>&int;</mo>
    </mrow>
    <mrow>
      <mn>0</mn>
    </mrow>
    <mrow>
      <mi>$b</mi>
    </mrow>
  </msubsup>
  <mo>(</mo>
  <mn>3</mn>
  <msup>
    <mrow>
      <mi>x</mi>
    </mrow>
    <mrow>
      <mn>2</mn>
    </mrow>
  </msup>
  <mo>+</mo>
  <mi>$c</mi>
  <mo>&InvisibleTimes;</mo>
  <mi>x</mi>
  <mo>)</mo>
  <mo>&DifferentialD;</mo>
  <mi>x</mi>
</math>
by taking a limit of the Riemann sum as 
<math>
  <mi>n</mi>
  <mo>&rarr;</mo>
  <mi>&infin;</mi>
</math>.
<br>
<br>
<6> &#160;@



qu.4.topic=4-estimating definite integrals from graphs@

qu.4.1.question=Determine
<math>
  <msubsup>
    <mo>&int;</mo>
    <mrow>
      <mn>0</mn>
    </mrow>
    <mrow>
      <mi>$r</mi>
    </mrow>
  </msubsup>
  <mrow>
    <mi>f</mi>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>&DifferentialD;</mo>
  <mi>x</mi>
</math>
using the graph of
<math><mi>f</mi></math>
given below.
<br>
<script>drawMaplePlot("plot([$s*$q*Heaviside($a-x)+$m*($b-x)*Heaviside(x-$a)*Heaviside($b+2*$c-x)-$q*Heaviside(x-$b-2*$c),$f],x=0..$r,color=[blue,seq(black,i=1..18)],linestyle=[SOLID,seq(DOT,i=1..18)],labels=[`x`,`f(x)`])");</script>@
qu.4.1.answer.num=$answer@
qu.4.1.answer.units=@
qu.4.1.showUnits=false@
qu.4.1.grading=exact_value@
qu.4.1.negStyle=minus@
qu.4.1.numStyle=thousands   @
qu.4.1.mode=Numeric@
qu.4.1.comment=The integral is the sum of the signed areas.  Subtract the negative area from the positive area.  The answer is $answer.@
qu.4.1.editing=useHTML@
qu.4.1.algorithm=$a=range(4,10);
$d=range(4,10);
condition:eq(int(($a+$d)/2),($a+$d)/2);
$c=range(1,2);
$s=range(2,3);
$q=range(1,4);
$m=$q/(2*$c);
$b=$a+2*$s*$c;
$r=$b+2*$c+$d;
$answer=$q*($s*$a+($s^2-1)*$c-$d);
$f=maple("seq([2*i,$q*y,y=-1..$s],i=1..18)");@



qu.5.topic=5-elementary antiderivatives@

qu.5.1.mode=Formula Mod C@
qu.5.1.comment=The answer is ${mathml("$answer")}.@
qu.5.1.editing=useHTML@
qu.5.1.algorithm=$a=range(1,9);
$b=range(1,9);
$c=range(1,9);
$m=range(2,5);
$mp=$m+1;
$bm=$b*$m;
$n=range(2,5);
$np=$n+1;
$p=range(2,5);
$pm=$p-1;
$function=$a*x^$n+$b*x^(1/"$m")+$c*x^(-$p);
$answer=($a/"$np")*x^($n+1)+($bm/"$mp")*x^("$mp/$m")-($c/"$pm")*x^(1-$p);@
qu.5.1.question=Find an antiderivative of &#160; ${mathml("$function")}.@
qu.5.1.answer=$answer@

qu.5.2.mode=Formula Mod C@
qu.5.2.comment=The answer is ${mathml("$answer")}.@
qu.5.2.editing=useHTML@
qu.5.2.algorithm=$a=range(1,9);
$b=range(-9,9);
$c=range(-9,9);
condition:not(eq($b*($b-1)*$c,0));
$function=$a*"e"^($b*x)+($c/x);
$answer=($a/"$b")*"e"^($b*x)+$c*ln(abs(x));@
qu.5.2.question=Find an antiderivative of &#160; ${mathml("$function")}.
<br>
Note that you must use "abs" for the absolute value function.@
qu.5.2.answer=$answer@

qu.5.3.mode=Formula Mod C@
qu.5.3.comment=The answer is ${mathml("$answer")}.@
qu.5.3.editing=useHTML@
qu.5.3.algorithm=$a=range(2,9);
$rone=rint(2);
$fone=switch($rone,sin($a*x),cos($a*x));
$ansone=switch($rone,cos($a*x),sin($a*x));
$sign=switch($rone,-1,1);
$ftwo=(sec x)^2;
$anstwo=tan x;
$answer=$sign*(1/"$a")*($ansone)+$anstwo;@
qu.5.3.question=Find an antiderivative of &#160; ${mathml($fone+$ftwo)}.@
qu.5.3.answer=$answer@

qu.5.4.mode=Formula Mod C@
qu.5.4.comment=The answer is ${mathml("$answer")}.  Note that the absolute value
is optional because ${mathml($w)} 
<math>
  <mo>&gt;</mo>
  <mn>0</mn>
</math>.@
qu.5.4.editing=useHTML@
qu.5.4.algorithm=$a=range(1,8);
$b=range(2,8);
$n=range(2,8,2);
$w=$a+$b*x^$n;
$wpf=if(eq($n,2),x,x^($n-1));
$wpc=$n*$b;
$function=($wpf)/($w);
$answer=("1"/($wpc))*ln($w);@
qu.5.4.question=Find an antiderivative of &#160; ${mathml($function)}.@
qu.5.4.answer=$answer@



qu.6.topic=6-definite integrals by the fundamental theorem@

qu.6.1.mode=Formula@
qu.6.1.comment=The answer is ${mathml("$answer")}.@
qu.6.1.editing=useHTML@
qu.6.1.algorithm=$a=range(1,2);
$b=range(2,4);
$c=range(2,9);
condition:gt($b,$a);
$r=rint(4);
$n=switch($r,1,2,-2,-3);
$m=switch($r,2,3,1,2);
$d=switch($r,2,3,$a*$b,2*$a^2*$b^2);
$function=if(eq($r,0),$c*$x,$c*x^$n);
$answer=($c*($b^$m-$a^$m))/"$d";@
qu.6.1.question=Compute 
<math>
  <msubsup>
    <mrow>
      <mo mathsize="150%">&int;</mo>
      <mtext>&ThinSpace;</mtext>
    </mrow>
    <mrow>
      <mn>$a</mn>
    </mrow>
    <mrow>
      <mn>$b</mn>
    </mrow>
  </msubsup>
</math> 
${mathml($function)} ${mathml(d*x)}.@
qu.6.1.answer=$answer@

qu.6.2.mode=Formula@
qu.6.2.comment=The answer is ${mathml("$answer")}.@
qu.6.2.editing=useHTML@
qu.6.2.algorithm=$b=range(2,9);
$c=range(2,9);
$a=range(-9,9);
condition:not(eq($a*($a-1),0));
$function=$c*"e"^($a*x);
$answer="($c/$a)*(e^($a*$b)-1)";@
qu.6.2.question=Compute 
<math>
  <msubsup>
    <mrow>
      <mo mathsize="150%">&int;</mo>
      <mtext>&ThinSpace;</mtext>
    </mrow>
    <mrow>
      <mn>0</mn>
    </mrow>
    <mrow>
      <mn>$b</mn>
    </mrow>
  </msubsup>
</math> 
${mathml("$function")} ${mathml(d*x)}.@
qu.6.2.answer=$answer@

qu.6.3.mode=Formula@
qu.6.3.comment=The answer is ${mathml("$answer")}.@
qu.6.3.editing=useHTML@
qu.6.3.algorithm=$a=range(2,5);
$b=range(6,9);
$c=range(2,9);
$x=switch(rint(6),"t","u","v","w","y","z");
$function=$c/$x;
$answer="$c*ln($b/$a)";@
qu.6.3.question=Compute 
<math>
  <msubsup>
    <mrow>
      <mo mathsize="150%">&int;</mo>
      <mtext>&ThinSpace;</mtext>
    </mrow>
    <mrow>
      <mn>$a</mn>
    </mrow>
    <mrow>
      <mn>$b</mn>
    </mrow>
  </msubsup>
</math> 
${mathml($function)} ${mathml(d*$x)}.@
qu.6.3.answer=$answer@

qu.6.4.mode=Formula@
qu.6.4.comment=The answer is ${mathml("$answer")}.@
qu.6.4.editing=useHTML@
qu.6.4.algorithm=$a=range(2,5);
$b=range(1,5);
$n=range(2,5);
$r=range(0,2);
$t=range(2,4);
condition:not(gt($t+$n,6));
$s=switch($r,1,1,-1);
$q=switch($r,7,1,$t^$n);
condition:gt($s*$b*$q,$s*$a);
$w=switch($r,$a+$b*x^$n,$b*x^$n-$a,$a-$b*x^$n);
$wpf=switch($r,if(eq($n,2),x,x^($n-1)),if(eq($n,2),x,x^($n-1)),if(eq($n,2),x,x^($n-1)));
$wpc=switch($r,$n*$b,$n*$b,-$n*$b);
$function=($wpf)/($w);
$from=switch($r,0,1,0);
$to=$t;
$wto=switch($r,$a+$b*$to^$n,$b*$to^$n-$a,$a-$b*$to^$n);
$wfrom=switch($r,$a,$b-$a,$a);
$answer=("1"/($wpc))*"ln($wto/$wfrom)";@
qu.6.4.question=Compute 
<math>
  <msubsup>
    <mrow>
      <mo mathsize="150%">&int;</mo>
      <mtext>&ThinSpace;</mtext>
    </mrow>
    <mrow>
      <mn>$from</mn>
    </mrow>
    <mrow>
      <mn>$to</mn>
    </mrow>
  </msubsup>
</math> 
${mathml($function)} ${mathml(d*x)}.@
qu.6.4.answer=$answer@



qu.7.topic=7-f values from f'@

qu.7.1.mode=Formula@
qu.7.1.comment=The answer is ${mathml("$answer")}.@
qu.7.1.editing=useHTML@
qu.7.1.algorithm=$c=range(1,9);
$n=range(2,5);
$np=$n+1;
$a=range(1,4);
$b=range(-8,8);
condition:not(gt($a+$n,6));
$function=$c*x^$n;
$C=($b*$np-$c*$a^($np))/"$np";
$answer=($c/"$np")*x^($np)+"$C";@
qu.7.1.question=Find an antiderivative of &#160; ${mathml("$function")}
that passes through the point
<math>
  <mo>(</mo>
  <mn>$a</mn>
  <mo>,</mo>
  <mn>$b</mn>
  <mo>)</mo>
</math>.@
qu.7.1.answer=$answer@

qu.7.2.question=An object is originally located at
<math>
  <mi>x</mi>
  <mo>=</mo>
  <mn>$x</mn>
</math>.
Beginning at time zero, the object moves along the 
<math><mi>x</mi></math> axis with velocity given by the graph below.
Determine the location of the object at time <math><mn>$r</mn></math>.
<br>
<script>drawMaplePlot("plot([$s*$q*Heaviside($a-x)+$m*($b-x)*Heaviside(x-$a)*Heaviside($b+2*$c-x)-$q*Heaviside(x-$b-2*$c),$f],x=0..$r,color=[blue,seq(black,i=1..18)],linestyle=[SOLID,seq(DOT,i=1..18)],labels=[`t`,`v(t)`])");</script>@
qu.7.2.answer.num=$answer@
qu.7.2.answer.units=@
qu.7.2.showUnits=false@
qu.7.2.grading=exact_value@
qu.7.2.negStyle=minus@
qu.7.2.numStyle=thousands   @
qu.7.2.mode=Numeric@
qu.7.2.comment=The net displacement is the integral of the velocity.  The answer is $answer.@
qu.7.2.editing=useHTML@
qu.7.2.algorithm=$x=range(1,10);
$a=range(4,10);
$d=range(4,10);
condition:eq(int(($a+$d)/2),($a+$d)/2);
$c=range(1,2);
$s=range(2,3);
$q=range(1,4);
$m=$q/(2*$c);
$b=$a+2*$s*$c;
$r=$b+2*$c+$d;
$answer=$x+$q*($s*$a+($s^2-1)*$c-$d);
$f=maple("seq([2*i,$q*y,y=-1..$s],i=1..18)");@

qu.7.3.mode=Formula@
qu.7.3.comment=The net displacement is the integral of the velocity.  The answer is ${mathml("$answer")}.@
qu.7.3.editing=useHTML@
qu.7.3.algorithm=$x=range(-5,5);
$a=range(-5,5);
$b=range(-5,5);
$bm=-$b;
$c=range(1,4);
$r=range(2,3);
condition:not(eq($x*($a^2+$b^2),0));
$function=if(lt($b,0),$a-$bm*t+$c*t^2,$a+$b*t+$c*t^2);
$answer=(6*$x+6*$a*$r+3*$b*$r^2+2*$c*$r^3)/"6";@
qu.7.3.question=An object is originally located at
<math>
  <mi>x</mi>
  <mo>=</mo>
  <mn>$x</mn>
</math>.
Beginning at time zero, the object moves along the 
<math><mi>x</mi></math> axis with velocity given by ${mathml($function)}.
Determine the exact location of the object at time <math><mn>$r</mn></math>.@
qu.7.3.answer=$answer@



qu.8.topic=8-average value@

qu.8.1.question=Determine the average value of 
<math><mi>f</mi></math>
on the interval 
<math>
  <mo>[</mo>
  <mn>0</mn>
  <mo>,</mo>
  <mn>$r</mn>
  <mo>]</mo> 
</math>.
<br>
Your answer should be correct to 2 decimal places.
<br>
<script>drawMaplePlot("plot([$s*$q*Heaviside($a-x)+$m*($b-x)*Heaviside(x-$a)*Heaviside($b+2*$c-x)-$q*Heaviside(x-$b-2*$c),$f],x=0..$r,color=[blue,seq(black,i=1..18)],linestyle=[SOLID,seq(DOT,i=1..18)],labels=[`x`,`f(x)`])");</script>@
qu.8.1.answer.num=$answer@
qu.8.1.answer.units=@
qu.8.1.showUnits=false@
qu.8.1.grading=toler_abs@
qu.8.1.err=.01@
qu.8.1.negStyle=minus@
qu.8.1.numStyle=thousands   @
qu.8.1.mode=Numeric@
qu.8.1.comment=The answer is $answer.@
qu.8.1.editing=useHTML@
qu.8.1.algorithm=$a=range(4,10);
$d=range(4,10);
condition:eq(int(($a+$d)/2),($a+$d)/2);
$c=range(1,2);
$s=range(2,3);
$q=range(1,4);
$m=$q/(2*$c);
$b=$a+2*$s*$c;
$r=$b+2*$c+$d;
$answer=$q*($s*$a+($s^2-1)*$c-$d)/$r;
$f=maple("seq([2*i,$q*y,y=-1..$s],i=1..18)");@

qu.8.2.mode=Formula@
qu.8.2.comment=The answer is ${mathml("$answer")}.@
qu.8.2.editing=useHTML@
qu.8.2.algorithm=$c=range(-4,4);
condition:not(eq($c,0));
$a=range(1,4);
$h=range(1,4);
$b=$a+$h;
$num=$a^2+$a*$b+$b^2;
$termtwo=$c*($a+$b);
$answer="$num/3+$termtwo";@
qu.8.2.question=Find the average value of &#160; ${mathml(x^2+2*$c*x)} &#160; on the interval 
<math>
  <mo>[</mo>
  <mn>$a</mn>
  <mo>,</mo>
  <mn>$b</mn>
  <mo>]</mo>
</math>.
<br>
Your answer should be exact.@
qu.8.2.answer=$answer@



qu.9.topic=9-derivatives of integrals@

qu.9.1.mode=Formula@
qu.9.1.comment=The answer is ${mathml($answera)} ${mathml($answerb)}.@
qu.9.1.editing=useHTML@
qu.9.1.algorithm=$a=range(0,2);
$b=range(2,9);
$c=range(2,9);
$d=range(2,9);
$m=range(2,6);
$n=range(2,6);
$f=switch(rint(3),"sin","cos","tan");
$functiona=ln($b*t^$n+$c);
$functionb=$f($d*t^-$m);
$answera=ln($b*x^$n+$c);
$answerb=$f($d*x^-$m);
$answer=$answera*$answerb;@
qu.9.1.question=Find the derivative of
<math>
  <msubsup>
    <mo mathsize=150%>&int;</mo>
    <mrow>
      <mi>$a</mi>
    </mrow>
    <mrow>
      <mi>x</mi>
    </mrow>
  </msubsup>
</math>
${mathml($functiona)} ${mathml($functionb)}
<math>
  <mtext>&ThinSpace;</mtext>
  <mi>dt</mi>
</math>.@
qu.9.1.answer=$answer@

qu.9.2.mode=Formula@
qu.9.2.comment=The answer is ${mathml($answer)}.@
qu.9.2.editing=useHTML@
qu.9.2.algorithm=$a=range(0,2);
$b=range(2,9);
$n=range(2,6);
$v=switch(rint(5),"u","v","w","y","z");
$function=sqrt(sec($b*$v^$n));
$answer=sqrt(sec($b*x^$n));@
qu.9.2.question=Find the derivative of
<math>
  <msubsup>
    <mo mathsize=150%>&int;</mo>
    <mrow>
      <mi>$a</mi>
    </mrow>
    <mrow>
      <mi>x</mi>
    </mrow>
  </msubsup>
</math>
${mathml($function)}
<math>
  <mtext>&ThinSpace;</mtext>
  <mi>d$v</mi>
</math>.@
qu.9.2.answer=$answer@