## 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.