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',
  '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:

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