Difference between revisions of "IndefiniteIntegrals1"

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<h2>Indefinite Integrals and General Antiderivatives</h2>
  
<h2>Indefinite Integrals and General Antiderivatives</h2>
   
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<p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
  
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[[File:IndefiniteIntegrals1.png|300px|thumb|right|Click to enlarge]]
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<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.
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<ul>
  
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<li>Download file: [[File:IndefiniteIntegrals1.txt]] (change the file extension from txt to pg when you save it)</li>
  
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<li>File location in NPL: <code>NationalProblemLibrary/FortLewis/Authoring/Templates/IntegralCalc/IndefiniteIntegrals1.pg</code></li>
  
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</ul>
  
 
</p>
  
</p>
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* 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]
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* 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]
   
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<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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Context("Numeric");
  
Context("Numeric");
   
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#
  
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$specific = Formula("e^x");
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# Specific antiderivative:
  
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# Marks correct e^x, e^x + pi, etc
  
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#
  
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$specific = Formula("e^x")->flags(upToConstant=>1);
  
   
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#
  
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# General antiderivative
  
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# Marks correct e^x + C, e^x + C - 3, e^x + K, etc.
  
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#
  
 
$general = FormulaUpToConstant("e^x");
  
$general = FormulaUpToConstant("e^x");
 
</pre>
  
</pre>
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<td style="background-color:#ffffcc;padding:7px;">
  
<td style="background-color:#ffffcc;padding:7px;">
 
<p>
  
<p>
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<b>Setup:</b>
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<b>Setup:</b>
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Examples of specific and general antiderivatives:
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<ul>
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<li>Specific antiderivatives: <code>e^x, e^x + pi</code></li>
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<li>General antiderivatives: <code>e^x + C, e^x + C - 3, e^x + K</code></li>
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</ul>
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</p>
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<p>
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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 <code>FormulaUpToConstant()</code> constructor provided by <code>parserFormulaUpToConstant.pl</code>.
 
</p>
  
</p>
 
</td>
  
</td>
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$showPartialCorrectAnswers = 1;
  
$showPartialCorrectAnswers = 1;
   
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ANS( $specific->cmp() );
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ANS( $specific->cmp(upToConstant=>1) );
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ANS( $general ->cmp() );
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ANS( $general->cmp() );
 
</pre>
  
</pre>
 
<td style="background-color:#eeccff;padding:7px;">
  
<td style="background-color:#eeccff;padding:7px;">
 
<p>
  
<p>
 
<b>Answer Evaluation:</b>
  
<b>Answer Evaluation:</b>
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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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Context()->texStrings;
  
Context()->texStrings;
 
BEGIN_SOLUTION
  
BEGIN_SOLUTION
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${PAR}SOLUTION:${PAR}
  
 
Solution explanation goes here.
  
Solution explanation goes here.
 
END_SOLUTION
  
END_SOLUTION
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[[Category:Top]]
  
[[Category:Top]]
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[[Category:Authors]]
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[[Category:Sample Problems]]
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[[Category:Subject Area Templates]]

Revision as of 13:49, 14 June 2015

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",
"AnswerFormatHelp.pl",
"parserFormulaUpToConstant.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. 

Context()->texStrings;
BEGIN_TEXT
Enter a specific antiderivative for \( e^x \): 
\{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
$BR
$BR
Enter the most general antiderivative for \( e^x \): 
\{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
END_TEXT
Context()->normalStrings;

Main Text: 

$showPartialCorrectAnswers = 1;

ANS( $specific->cmp(upToConstant=>1) );

ANS( $general->cmp() );

Answer Evaluation: For the specific antiderivative, we must use upToConstant=>1, otherwise the only answer that will be marked correct will be e^x. 

Context()->texStrings;
BEGIN_SOLUTION
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();

Solution:

Templates by Subject Area

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