IndefiniteIntegrals1

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Indefinite Integrals and General Antiderivatives

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


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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:

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