IndefiniteIntegrals1: Difference between revisions

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{{historical}}
<p style="font-size: 120%;font-weight:bold">This problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/IntegralCalc/IndefiniteIntegrals.html a newer version of this problem]</p>
<h2>Indefinite Integrals and General Antiderivatives</h2>
<h2>Indefinite Integrals and General Antiderivatives</h2>


<p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
[[File:IndefiniteIntegrals1.png|300px|thumb|right|Click to enlarge]]
<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;">
This PG code shows how to check answers that are indefinite integrals or general antiderivatives.
This PG code shows how to check answers that are indefinite integrals or general antiderivatives.
<ul>
<li>Download file: [[File:IndefiniteIntegrals1.txt]] (change the file extension from txt to pg when you save it)</li>
<li>File location in NPL: <code>NationalProblemLibrary/FortLewis/Authoring/Templates/IntegralCalc/IndefiniteIntegrals1.pg</code></li>
</ul>
</p>
</p>
* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/IntegralCalc/IndefiniteIntegrals1.pg FortLewis/Authoring/Templates/IntegralCalc/IndefiniteIntegrals1.pg]
* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/IntegralCalc/IndefiniteIntegrals1_PGML.pg FortLewis/Authoring/Templates/IntegralCalc/IndefiniteIntegrals1_PGML.pg]


<br clear="all" />
<p style="text-align:center;">
<p style="text-align:center;">
[[SubjectAreaTemplates|Templates by Subject Area]]
[[SubjectAreaTemplates|Templates by Subject Area]]
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<tr valign="top">
<tr valign="top">
<th> PG problem file </th>
<th style="width: 40%"> PG problem file </th>
<th> Explanation </th>
<th> Explanation </th>
</tr>
</tr>
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loadMacros(
loadMacros(
"PGstandard.pl",
  'PGstandard.pl',
"MathObjects.pl",
  'MathObjects.pl',
"AnswerFormatHelp.pl",
  'parserFormulaUpToConstant.pl',
"parserFormulaUpToConstant.pl",
  'PGML.pl',
  'PGcourse.pl'
);
);


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<p>
<p>
<b>Setup:</b>
<b>Setup:</b>
The specific antiderivative should mark correct answers such as <code>e^x, e^x + pi</code>, etc.  The general antiderivative should mark correct answers such as <code>e^x + C, e^x + C - 3, e^x + K</code>, etc.
Examples of specific and general antiderivatives:
<ul>
<li>Specific antiderivatives: <code>e^x, e^x + pi</code></li>
<li>General antiderivatives: <code>e^x + C, e^x + C - 3, e^x + K</code></li>
</ul>
</p>
</p>
<p>
<p>
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<td style="background-color:#ffdddd;border:black 1px dashed;">
<td style="background-color:#ffdddd;border:black 1px dashed;">
<pre>
<pre>
Context()->texStrings;
BEGIN_PGML
BEGIN_TEXT
+ Enter a specific antiderivative for [` e^x `]: [____________]{$specific->cmp(upToConstant=>1)}
Enter a specific antiderivative for \( e^x \):  
 
\{ ans_rule(20) \}
+ Enter the most general antiderivative for [` e^x `]: [____________]{$general}
\{ AnswerFormatHelp("formulas") \}
 
$BR
[@ helpLink('formulas') @]*
$BR
END_PGML
Enter the most general antiderivative for \( e^x \):  
\{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
END_TEXT
Context()->normalStrings;
</pre>
</pre>
<td style="background-color:#ffcccc;padding:7px;">
<td style="background-color:#ffcccc;padding:7px;">
<p>
<p>
<b>Main Text:</b>
<b>Main Text:</b>
</p>
</td>
</tr>
<!-- Answer evaluation section -->
<tr valign="top">
<td style="background-color:#eeddff;border:black 1px dashed;">
<pre>
$showPartialCorrectAnswers = 1;
ANS( $specific->cmp(upToConstant=>1) );
ANS( $general->cmp() );
</pre>
<td style="background-color:#eeccff;padding:7px;">
<p>
<b>Answer Evaluation:</b>
For the specific antiderivative, we must use <code>upToConstant=>1</code>, otherwise the only answer that will be marked correct will be <code>e^x</code>.
</p>
</p>
</td>
</td>
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<td style="background-color:#ddddff;border:black 1px dashed;">
<td style="background-color:#ddddff;border:black 1px dashed;">
<pre>
<pre>
Context()->texStrings;
BEGIN_PGML_SOLUTION
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
Solution explanation goes here.
END_SOLUTION
END_PGML_SOLUTION
Context()->normalStrings;
 
COMMENT('MathObject version.');


ENDDOCUMENT();
ENDDOCUMENT();
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[[Category:Top]]
[[Category:Top]]
[[Category:Authors]]
[[Category:Sample Problems]]
[[Category:Subject Area Templates]]

Latest revision as of 10:13, 18 July 2023

This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with a newer version of this problem


Indefinite Integrals and General Antiderivatives

Click to enlarge

This PG code shows how to check answers that are indefinite integrals or general antiderivatives.


Templates by Subject Area

PG problem file Explanation

Problem tagging data

Problem tagging: 

DOCUMENT();

loadMacros(
  'PGstandard.pl',
  'MathObjects.pl',
  'parserFormulaUpToConstant.pl',
  'PGML.pl',
  'PGcourse.pl'
);

TEXT(beginproblem());

Initialization: 

Context("Numeric");

$specific = Formula("e^x");

$general = FormulaUpToConstant("e^x");

Setup: Examples of specific and general antiderivatives:

  • Specific antiderivatives: e^x, e^x + pi
  • General antiderivatives: e^x + C, e^x + C - 3, e^x + K

The specific antiderivative is an ordinary formula, and we check this answer, we will specify that it be a formula evaluated up to a constant (see the Answer Evaluation section below). For the general antiderivative, we use the FormulaUpToConstant() constructor provided by parserFormulaUpToConstant.pl. 

BEGIN_PGML
+ Enter a specific antiderivative for [` e^x `]: [____________]{$specific->cmp(upToConstant=>1)}

+ Enter the most general antiderivative for [` e^x `]: [____________]{$general}

[@ helpLink('formulas') @]*
END_PGML

Main Text: 

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution:

Templates by Subject Area

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