View of /trunk/NationalProblemLibrary/UMN/calculusStewartCCC/s_6_2_prob01.pg

    1 #DESCRIPTION
    2 ##  Calculus: Volumes
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('calculus', 'volumes')
    6 
    7 ## DBsubject('Calculus')
    8 ## DBchapter('Applications of Integration')
    9 ## DBsection('Volumes')
   10 ## Date('03/03/2010')
   11 ## Author('Justin Sukiennik')
   12 ## Institution('University of Minnesota')
   13 ## TitleText1('Calculus: Concepts and Contexts')
   14 ## EditionText1('4 Custom UMTYMP Ed.')
   15 ## AuthorText1('Stewart')
   16 ## Section1('6.2')
   17 ## Problem1('')
   18 
   19 #####################################################################
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23   "PGstandard.pl",
   24   "MathObjects.pl",
   25   "PGcourse.pl",
   26 );
   27 
   28 #####################################################################
   29 
   30 $showPartialCorrectAnswers = 1;
   31 TEXT(beginproblem());
   32 
   33 
   34 Context("Numeric");
   35 
   36 $n = random(2,6,2);
   37 $c = random(2,8,1);
   38 
   39 $an = Compute("2*pi*(2*$c - 1 - 2*$c/($n+1) + 1/(2*$n + 1))")->reduce;
   40 
   41 $ans = Compute("$an");
   42 
   43 #####################################################################
   44 
   45 Context()->texStrings;
   46 BEGIN_TEXT
   47 Find the volume of the solid obtained by rotating the region bounded by \(y = x^{$n}\) and \(y = 1\) about the line \(y = $c.\)$PAR
   48 Volume = \{ans_rule(20) \}
   49 END_TEXT
   50 
   51 #####################################################################
   52 
   53 ANS(($ans)->cmp());
   54 
   55 ENDDOCUMENT();        # This should be the last executable line in the problem.