#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.