https://webwork.maa.org/mediawiki_new/index.php?title=DoubleIntegral1&feed=atom&action=history
DoubleIntegral1 - Revision history
2024-03-28T11:00:06Z
Revision history for this page on the wiki
MediaWiki 1.34.0
https://webwork.maa.org/mediawiki_new/index.php?title=DoubleIntegral1&diff=23795&oldid=prev
Pstaabp: add historical tag and give links to newer problems.
2023-07-18T10:29:55Z
<p>add historical tag and give links to newer problems.</p>
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Pstaabp
https://webwork.maa.org/mediawiki_new/index.php?title=DoubleIntegral1&diff=23453&oldid=prev
Pstaabp: switch to PGML.
2023-03-11T12:15:44Z
<p>switch to PGML.</p>
<a href="https://webwork.maa.org/mediawiki_new/index.php?title=DoubleIntegral1&diff=23453&oldid=9219">Show changes</a>
Pstaabp
https://webwork.maa.org/mediawiki_new/index.php?title=DoubleIntegral1&diff=9219&oldid=prev
Paultpearson: PGML example link
2015-06-14T19:12:19Z
<p>PGML example link</p>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/IntegralCalcMV/DoubleIntegral1.pg FortLewis/Authoring/Templates/IntegralCalcMV/DoubleIntegral1.pg]</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/IntegralCalcMV/DoubleIntegral1.pg FortLewis/Authoring/Templates/IntegralCalcMV/DoubleIntegral1.pg]</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/IntegralCalcMV/DoubleIntegral1_PGML.pg FortLewis/Authoring/Templates/IntegralCalcMV/DoubleIntegral1_PGML.pg]</div></td>
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Paultpearson
https://webwork.maa.org/mediawiki_new/index.php?title=DoubleIntegral1&diff=9218&oldid=prev
Paultpearson at 21:25, 16 June 2013
2013-06-16T21:25:15Z
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This PG code shows how to allow students to set up a double integral and integrate in either order.</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Download file: [[File:DoubleIntegral1.txt]] (change the file extension from txt to pg when you save it)</div></td>
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Paultpearson
https://webwork.maa.org/mediawiki_new/index.php?title=DoubleIntegral1&diff=9217&oldid=prev
Paultpearson at 21:34, 3 January 2012
2012-01-03T21:34:09Z
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Paultpearson
https://webwork.maa.org/mediawiki_new/index.php?title=DoubleIntegral1&diff=9216&oldid=prev
Pearson at 18:34, 20 December 2010
2010-12-20T18:34:53Z
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><b>Setup:</b> </div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are two separate cases: integrating with respect to <code>dx dy</code> (which we call case 0) or with respect to <code>dy dx</code> (which we call case 1). The zeroth and first entries in each of the arrays <code>@id, @od, @A, @B, @C, @D</code> hold the values for case 0 and case 1, respectively. We used constant limits of integration to keep this example easy to follow, but we encourage you to write questions over non-rectangular regions.</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are two separate cases: integrating with respect to <code>dx dy</code> (which we call case 0) or with respect to <code>dy dx</code> (which we call case 1). The zeroth and first entries in each of the arrays <code>@id, @od, @A, @B, @C, @D</code> hold the values for case 0 and case 1, respectively. We used constant limits of integration to keep this example easy to follow, but we encourage you to write questions over non-rectangular regions.</div></td>
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Pearson
https://webwork.maa.org/mediawiki_new/index.php?title=DoubleIntegral1&diff=9215&oldid=prev
Pearson: Created page with '<h2>Setting up a Double Integral</h2> Click to enlarge <p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;"> Th…'
2010-12-20T18:32:32Z
<p>Created page with '<h2>Setting up a Double Integral</h2> <a href="/wiki/File:DoubleIntegral1.png" title="File:DoubleIntegral1.png">300px|thumb|right|Click to enlarge</a> <p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;"> Th…'</p>
<p><b>New page</b></p><div><h2>Setting up a Double Integral</h2><br />
<br />
[[File:DoubleIntegral1.png|300px|thumb|right|Click to enlarge]]<br />
<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;"><br />
This PG code shows how to allow students to set up a double integral and integrate in either order.<br />
</p><br />
* Download file: [[File:DoubleIntegral1.txt]] (change the file extension from txt to pg when you save it)<br />
* File location in NPL: <code>FortLewis/Authoring/Templates/IntegralCalcMV/DoubleIntegral1.pg</code><br />
<br />
<br clear="all" /><br />
<p style="text-align:center;"><br />
[[SubjectAreaTemplates|Templates by Subject Area]]<br />
</p><br />
<br />
<table cellspacing="0" cellpadding="2" border="0"><br />
<br />
<tr valign="top"><br />
<th> PG problem file </th><br />
<th> Explanation </th><br />
</tr><br />
<br />
<br />
<!-- Problem tagging section --><br />
<br />
<tr valign="top"><br />
<td style="background-color:#eeeeee;border:black 1px dashed;"><br />
[http://webwork.maa.org/wiki/Tagging_Problems Problem tagging data]<br />
</td><br />
<td style="background-color:#eeeeee;padding:7px;"><br />
<p><br />
<b>Problem tagging:</b><br />
</p><br />
</td><br />
</tr><br />
<br />
<br />
<!-- Initialization section --><br />
<br />
<tr valign="top"><br />
<td style="background-color:#ddffdd;border:black 1px dashed;"><br />
<pre><br />
DOCUMENT(); <br />
<br />
loadMacros(<br />
"PGstandard.pl",<br />
"MathObjects.pl",<br />
"parserMultiAnswer.pl",<br />
);<br />
<br />
TEXT(beginproblem());<br />
</pre><br />
</td><br />
<td style="background-color:#ddffdd;padding:7px;"><br />
<p><br />
<b>Initialization:</b><br />
Since there are multiple answer blanks that are dependent upon each other, we use <code>parserMultiAnswer.pl</code>.<br />
</p><br />
</td><br />
</tr><br />
<br />
<br />
<!-- Setup section --><br />
<br />
<tr valign="top"><br />
<td style="background-color:#ffffdd;border:black 1px dashed;"><br />
<pre><br />
Context("Numeric");<br />
Context()->variables->are(<br />
x=>"Real",dx=>"Real",<br />
y=>"Real",dy=>"Real");<br />
Context()->flags->set(reduceConstants=>0);<br />
<br />
#<br />
# limits of integration<br />
#<br />
$a = random(1,5,1);<br />
$b = $a + random(1,4,1);<br />
do { $c = random(1,5,1); } until ($c != $a);<br />
do { $d = $c + random(1,4,1); } until ($d != $b);<br />
<br />
#<br />
# integrand and volume<br />
#<br />
$f = Formula("x*y");<br />
$V = Formula("($b^2-$a^2) * ($d^2-$c^2) / 4");<br />
<br />
<br />
#<br />
# differentials and limits of integration<br />
#<br />
# Case 0, element 0 of each array below, is <br />
# if the order of integration is dx dy<br />
#<br />
# Case 1, element 1 of each array below, is<br />
# if the order of integration is dy dx<br />
# <br />
# "id" and "od" stand for inner and outer differential<br />
#<br />
@id = (Formula("dx"),Formula("dy")); # (case 0, case 1)<br />
@od = (Formula("dy"),Formula("dx")); # (case 0, case 1)<br />
#<br />
# A = outer integral, lower limit<br />
# B = outer integral, upper limit<br />
# C = inner integral, lower limit<br />
# D = inner integral, upper limit<br />
#<br />
@A = (Formula("$c"),Formula("$a")); # (case 0, case 1)<br />
@B = (Formula("$d"),Formula("$b")); # (case 0, case 1)<br />
@C = (Formula("$a"),Formula("$c")); # (case 0, case 1)<br />
@D = (Formula("$b"),Formula("$d")); # (case 0, case 1)<br />
<br />
<br />
$multians = MultiAnswer( $f, $id[0], $od[0], $A[0], $B[0], $C[0], $D[0] )->with(<br />
singleResult => 1,<br />
checker => sub {<br />
my ( $correct, $student, $self ) = @_;<br />
my ( $fstu, $idstu, $odstu, $Astu, $Bstu, $Cstu, $Dstu ) = @{$student};<br />
if ( <br />
( <br />
$f == $fstu &&<br />
$id[0] == $idstu && <br />
$od[0] == $odstu &&<br />
$A[0] == $Astu &&<br />
$B[0] == $Bstu &&<br />
$C[0] == $Cstu &&<br />
$D[0] == $Dstu <br />
)<br />
||<br />
(<br />
$f == $fstu &&<br />
$id[1] == $idstu && <br />
$od[1] == $odstu &&<br />
$A[1] == $Astu &&<br />
$B[1] == $Bstu &&<br />
$C[1] == $Cstu &&<br />
$D[1] == $Dstu <br />
)<br />
) {<br />
return 1;<br />
} elsif (<br />
(<br />
$f == $fstu &&<br />
$id[0] == $idstu && <br />
$od[0] == $odstu &&<br />
($A[0] != $Astu || $B[0] != $Bstu) &&<br />
$C[0] == $Cstu &&<br />
$D[0] == $Dstu <br />
) <br />
||<br />
(<br />
$f == $fstu &&<br />
$id[1] == $idstu && <br />
$od[1] == $odstu &&<br />
($A[1] != $Astu || $B[1] != $Bstu) &&<br />
$C[1] == $Cstu &&<br />
$D[1] == $Dstu <br />
) <br />
||<br />
(<br />
$f == $fstu &&<br />
$id[0] == $idstu && <br />
$od[0] == $odstu &&<br />
$A[0] == $Astu &&<br />
$B[0] == $Bstu &&<br />
($C[0] != $Cstu || $D[0] != $Dstu) <br />
) <br />
||<br />
(<br />
$f == $fstu &&<br />
$id[1] == $idstu && <br />
$od[1] == $odstu &&<br />
$A[1] == $Astu &&<br />
$B[1] == $Bstu &&<br />
($C[1] != $Cstu || $D[1] != $Dstu) <br />
) <br />
) {<br />
$self->setMessage(1,"Check your limits of integration.");<br />
return 0.94;<br />
} elsif (<br />
(<br />
$f == $fstu &&<br />
$id[0] == $idstu && <br />
$od[0] == $odstu &&<br />
($A[0] != $Astu || $B[0] != $Bstu) &&<br />
($C[0] != $Cstu || $D[0] != $Dstu) <br />
) <br />
||<br />
(<br />
$f == $fstu &&<br />
$id[1] == $idstu && <br />
$od[1] == $odstu &&<br />
($A[1] != $Astu || $B[1] != $Bstu) &&<br />
($C[1] != $Cstu || $D[1] != $Dstu) <br />
) <br />
) {<br />
$self->setMessage(1,<br />
"Check your limits of integration and order of integration.");<br />
return 0.47;<br />
} else {<br />
return 0;<br />
}<br />
}<br />
);<br />
</pre><br />
</td><br />
<td style="background-color:#ffffcc;padding:7px;"><br />
<p><br />
<b>Setup:</b> <br />
There are two separate cases: integrating with respect to <code>dx dy</code> (which we call case 0) or with respect to <code>dy dx</code> (which we call case 1). The zeroth and first entries in each of the arrays <code>@id, @od, @A, @B, @C, @D</code> hold the values for case 0 and case 1, respectively. We used constant limits of integration to keep this example easy to follow, but we encourage you to write questions over non-rectangular regions.<br />
</p><br />
</td><br />
</tr><br />
<br />
<!-- Main text section --><br />
<br />
<tr valign="top"><br />
<td style="background-color:#ffdddd;border:black 1px dashed;"><br />
<pre><br />
Context()->texStrings;<br />
BEGIN_TEXT<br />
Set up a double integral in rectangular coordinates<br />
for calculating the volume of the solid under the <br />
graph of the function \( f(x,y) = $f \) over the <br />
region \( $a \leq x \leq $b \) and \( $c \leq y \leq $d \).<br />
$BR<br />
$BR<br />
${BITALIC}Instructions:${EITALIC}<br />
Please enter the integrand in the first answer box. <br />
Depending on the order of integration you choose, <br />
enter ${BITALIC}dx${EITALIC} and ${BITALIC}dy${EITALIC} <br />
in either order into the second and third answer boxes <br />
with only one ${BITALIC}dx${EITALIC} or <br />
${BITALIC}dy${EITALIC} in each box. Then, enter the limits of <br />
integration and evaluate the integral to find the volume. <br />
$BR<br />
$BR<br />
\( \displaystyle \int_A^B \int_C^D \) <br />
\{ $multians->ans_rule(40) \}<br />
\{ $multians->ans_rule(5) \}<br />
\{ $multians->ans_rule(5) \}<br />
$BR<br />
$BR<br />
A = \{ $multians->ans_rule(20) \} $BR<br />
B = \{ $multians->ans_rule(20) \} $BR<br />
C = \{ $multians->ans_rule(20) \} $BR<br />
D = \{ $multians->ans_rule(20) \}<br />
$BR<br />
$BR<br />
Volume = \{ ans_rule(40) \}<br />
END_TEXT<br />
Context()->normalStrings;<br />
</pre><br />
<td style="background-color:#ffcccc;padding:7px;"><br />
<p><br />
<b>Main Text:</b><br />
The only interesting thing to note here is that you must use <code>$multians-&gt;ans_rule(20)</code> to make each answer blank known to the object <code>$multians</code>.<br />
</p><br />
</td><br />
</tr><br />
<br />
<!-- Answer evaluation section --><br />
<br />
<tr valign="top"><br />
<td style="background-color:#eeddff;border:black 1px dashed;"><br />
<pre><br />
$showPartialCorrectAnswers = 1;<br />
<br />
ANS( $multians->cmp() );<br />
ANS( $V->cmp() );<br />
</pre><br />
<td style="background-color:#eeccff;padding:7px;"><br />
<p><br />
<b>Answer Evaluation:</b><br />
</p><br />
</td><br />
</tr><br />
<br />
<!-- Solution section --><br />
<br />
<tr valign="top"><br />
<td style="background-color:#ddddff;border:black 1px dashed;"><br />
<pre><br />
Context()->texStrings;<br />
BEGIN_SOLUTION<br />
${PAR}SOLUTION:${PAR}<br />
Solution explanation goes here.<br />
END_SOLUTION<br />
Context()->normalStrings;<br />
<br />
<br />
COMMENT('MathObject version. Allows integration in either order.');<br />
ENDDOCUMENT();<br />
</pre><br />
<td style="background-color:#ddddff;padding:7px;"><br />
<p><br />
<b>Solution:</b><br />
</p><br />
</td><br />
</tr><br />
<br />
</table><br />
<br />
<p style="text-align:center;"><br />
[[SubjectAreaTemplates|Templates by Subject Area]]<br />
</p><br />
<br />
[[Category:Top]]<br />
[[Category:Authors]]</div>
Pearson