## DESCRIPTION ## Evaluate a Trig Integral ## ENDDESCRIPTION ## KEYWORDS('Indefinite', 'Trig Integral') ## Tagged by nhamblet ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Trigonometric Integrals') ## Date('8/23/07') ## Author('K. Lesh') ## Institution('Union') ## TitleText1('Calculus') ## EditionText1('7') ## AuthorText1('Anton') ## Section1('8.3') ## Problem1('08') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGstandard.pl", "PGunion.pl", # Union College utilities "MathObjects.pl", "PGcourse.pl", # Customization file for the course ); TEXT(beginproblem()); ################################### # Setup $n = random(3,9,2);$integrand=Formula(" tan^{3}(x) sec^{$n}(x) "); ################################### # Main text Context()->texStrings; BEGIN_TEXT Evaluate the indefinite integral.$PAR $$\displaystyle\int integrand \, dx$$ = \{ans_rule(50)\} $$+ C$$. END_TEXT Context()->normalStrings; ################################### # Answers $showPartialCorrectAnswers = 1; Context()->flags->set(reduceConstants=>0);$power2 = $n+2;$antideriv = Formula( "(1/$power2)(sec(x))^{$power2} - (1/$n)(sec(x))^$n") ->with(limits => [0,1]); ANS(\$antideriv->cmp(upToConstant=>1)); ################################### COMMENT('MathObject version'); ENDDOCUMENT();