## Original: /Library/ma123DB/set4/s7_8_17.pg ##KEYWORDS('integrals', 'improper') ##DESCRIPTION ## Determine if an improper integral converges and evaluate it. ##ENDDESCRIPTION ## Shotwell cleaned ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Improper Integrals') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.8') ## Problem1('17') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGstandard.pl", "MathObjects.pl", "parserPopUp.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1; Context("Numeric"); Context()->variables->add(n=>'Real'); Context()->variables->set(n=>{limits=>{1,2,3,4}});$popup1 = PopUp(["?","yes","no"],"no"); $popup2 =$popup1; $func = Compute("sin(x)")->reduce; Context()->texStrings; BEGIN_TEXT For $$n$$ a positive integer, compute $$\displaystyle \int_{0}^{2 n \pi} func dx$$.$BR $$\displaystyle \int_{0}^{2 n \pi} func dx =$$\{ans_rule(30)\} $PAR Can you deduce the nature (i.e., convergent or divergent) of $$\displaystyle \int_{0}^{\infty} func dx$$ from this?$BR Answer: \{$popup1->menu\}$PAR Now compute $$\displaystyle \int_{0}^{n \pi} func dx$$. $BR $$\displaystyle \int_{0}^{n \pi} func dx =$$\{ans_rule(30)\}$PAR Does $$\displaystyle \int_{0}^{\infty} func dx$$ converge? $BR Answer: \{$popup2->menu\} $PAR END_TEXT Context()->normalStrings;$ans1 = Compute("0"); $ans2 = Compute("1-(-1)^n"); ANS($ans1->cmp, $popup1->cmp,$ans2->cmp, \$popup2->cmp ); ENDDOCUMENT(); # This should be the last executable line in the problem.