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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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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.