Indefinite Integrals

Indefinite integrals

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Complete Code

Download file: IndefiniteIntegrals.pg

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

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

Preamble

The macro parserFormulaUpToConstant.pl will allow the entry of formula with a general constant like the antiderivative.

# Specific antiderivative:  Marks correct e^x, e^x + pi, etc
$specific = Formula('e^x');

#  General antiderivative: Marks correct e^x + C, e^x + C - 3, e^x + K, etc.
$general = FormulaUpToConstant('e^x');

Setup

The specific antiderivative is an ordinary formula. When the cmp method is called for this answer the upToConstant option will be passed to specify that it be a formula evaluated up to a constant.

For the general antiderivative the FormulaUpToConstant method provided by parserFormulaUpToConstant.pl is used.

BEGIN_PGML
a. Enter a specific antiderivative for [`e^x`]:
[_]{ $specific->cmp(upToConstant => 1) }{10}

b. Enter the most general antiderivative for [`e^x`]:
[_]{$general}{10}
END_PGML

Statement

The option upToConstant => 1 is passed to the cmp method for the first answer rule to specify that the any answer that differs from the given answer only by a constant is to be accepted.

The second answer $general is created with FormulaUpToConstant which means that an arbitrary additive constant must be included in the answer. Any letter aside that is not a variable in the context or e can be used to represent the arbitrary constant.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.