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    1 ## DESCRIPTION
    2 ## Calculus: Volumes by Cylindrical Shells
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus', 'integrals', 'volumes', 'cylindrical shells')
    6 ## Tagged by XW
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Integration')
   10 ## DBsection('Volumes by Cylindrical Shells')
   11 ## Date('6/5/2005')
   12 ## Author('Jeff Holt')
   13 ## Institution('UVA')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('5e')
   16 ## AuthorText1('Stewart')
   17 ## Section1('6.3')
   18 ## Problem1('35')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a=random(-8, 8,1);
   34 $b=random($a+1,9,1);
   35 $p=$a*$b;
   36 $s=-($a+$b);
   37 $soln = $PI*(-$a**5/30+$a**4 * $b/6 -$a**3 * $b**2/3 + $a**2 * $b**3/3 -$a*$b**4/6+$b**5/30);
   38 
   39 TEXT(EV2(<<EOT));
   40 
   41 Find the volume of the solid obtained by rotating the region bounded by the
   42 given curves about the specified axis.
   43 \[ y=x^2 ? {$s} x ? {$p}, \quad y = 0;  \]
   44  about the \(x\)-axis.
   45 
   46 $BR
   47 Volume = \{ans_rule( 25) \}
   48 $BR
   49 EOT
   50 ANS(num_cmp($soln));
   51 
   52 ENDDOCUMENT();        # This should be the last executable line in the problem.