#DESCRIPTION
##  Calculus: Volumes
##ENDDESCRIPTION

##KEYWORDS('calculus', 'volumes')

## DBsubject('Calculus')
## DBchapter('Applications of Integration')
## DBsection('Volumes')
## Date('03/03/2010')
## Author('Justin Sukiennik')
## Institution('University of Minnesota')
## TitleText1('Calculus: Concepts and Contexts')
## EditionText1('4 Custom UMTYMP Ed.')
## AuthorText1('Stewart')
## Section1('6.2')
## Problem1('')

#####################################################################
DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "PGcourse.pl", 
);

#####################################################################

$showPartialCorrectAnswers = 1;
TEXT(beginproblem());


Context("Numeric");

$n = random(2,6,2);
$c = random(2,8,1);

$an = Compute("2*pi*(2*$c - 1 - 2*$c/($n+1) + 1/(2*$n + 1))")->reduce;

$ans = Compute("$an");

#####################################################################

Context()->texStrings;
BEGIN_TEXT
Find the volume of the solid obtained by rotating the region bounded by \(y = x^{$n}\) and \(y = 1\) about the line \(y = $c.\)$PAR
Volume = \{ans_rule(20) \}
END_TEXT

#####################################################################

ANS(($ans)->cmp());

ENDDOCUMENT();        # This should be the last executable line in the problem.