[npl] / trunk / NationalProblemLibrary / UMN / calculusStewartCCC / s_6_2_prob01.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Tue Aug 16 17:21:05 2011 UTC (21 months ago) by aubreyja
File size: 1377 byte(s)
`Moving UMN contributions to NPL`

```    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
23   "PGstandard.pl",
24   "MathObjects.pl",
25   "PGcourse.pl",
26 );
27
28 #####################################################################
29
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.
```