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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;"> |
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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> |
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</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" /> |
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<p style="text-align:center;"> |
<p style="text-align:center;"> |
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[[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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− | $specific = Formula("e^x")->flags(upToConstant=>1); |
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− | # |
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− | # General antiderivative |
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− | # Marks correct e^x + C, e^x + C - 3, e^x + K, etc. |
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− | # |
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$general = FormulaUpToConstant("e^x"); |
$general = FormulaUpToConstant("e^x"); |
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</pre> |
</pre> |
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<td style="background-color:#ffffcc;padding:7px;"> |
<td style="background-color:#ffffcc;padding:7px;"> |
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<p> |
<p> |
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− | <b>Setup:</b> |
+ | <b>Setup:</b> |
+ | Examples of specific and general antiderivatives: |
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+ | <ul> |
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+ | <li>Specific antiderivatives: <code>e^x, e^x + pi</code></li> |
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+ | <li>General antiderivatives: <code>e^x + C, e^x + C - 3, e^x + K</code></li> |
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+ | </ul> |
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+ | </p> |
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+ | <p> |
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+ | The specific antiderivative is an ordinary formula, and we check this answer, we will specify that it be a formula evaluated up to a constant (see the Answer Evaluation section below). For the general antiderivative, we use the <code>FormulaUpToConstant()</code> constructor provided by <code>parserFormulaUpToConstant.pl</code>. |
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</p> |
</p> |
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</td> |
</td> |
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$showPartialCorrectAnswers = 1; |
$showPartialCorrectAnswers = 1; |
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− | ANS( $specific->cmp() ); |
+ | ANS( $specific->cmp(upToConstant=>1) ); |
− | + | ||
+ | ANS( $general->cmp() ); |
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</pre> |
</pre> |
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<td style="background-color:#eeccff;padding:7px;"> |
<td style="background-color:#eeccff;padding:7px;"> |
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<p> |
<p> |
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<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>. |
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</p> |
</p> |
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</td> |
</td> |
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Context()->texStrings; |
Context()->texStrings; |
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BEGIN_SOLUTION |
BEGIN_SOLUTION |
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− | ${PAR}SOLUTION:${PAR} |
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Solution explanation goes here. |
Solution explanation goes here. |
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END_SOLUTION |
END_SOLUTION |
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[[Category:Top]] |
[[Category:Top]] |
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− | [[Category: |
+ | [[Category:Sample Problems]] |
+ | [[Category:Subject Area Templates]] |
Revision as of 13:49, 14 June 2015
Indefinite Integrals and General Antiderivatives
This PG code shows how to check answers that are indefinite integrals or general antiderivatives.
- File location in OPL: FortLewis/Authoring/Templates/IntegralCalc/IndefiniteIntegrals1.pg
- PGML location in OPL: FortLewis/Authoring/Templates/IntegralCalc/IndefiniteIntegrals1_PGML.pg
PG problem file | Explanation |
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Problem tagging: |
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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:
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 |
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 |
Context()->texStrings; BEGIN_SOLUTION Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT(); |
Solution: |