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# View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S5/problem_2.pg

Tue Jun 26 21:45:47 2007 UTC (5 years, 11 months ago) by jjholt
File size: 1098 byte(s)
Updated tags. --JJH


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Gaussian' 'distribution' 'integral')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Integrals over Curves and Surfaces')
10 ## DBsection('Line Integrals')
11 ## Date('')
12 ## Author('')
13 ## Institution('Dartmouth')
14 ## TitleText1('Basic Multivariable Calculus')
15 ## EditionText1('')
16 ## AuthorText1('Marsden, Tromba, Weinstein')
17 ## Section1('6.1')
18 ## Problem1('')
19
20 DOCUMENT();
22            "PGbasicmacros.pl",
23            "PGchoicemacros.pl",
25            "PGauxiliaryFunctions.pl",
26            "PGgraphmacros.pl",
27            "Dartmouthmacros.pl");
28
29
30 ## Do NOT show partial correct answers
31 $showPartialCorrectAnswers = 1; 32 33 ## Lots of set up goes here 34$sigma = random(2,10,1);
35
36 ## Ok, we are ready to begin the problem...
37 ##
38 TEXT(beginproblem());
39
40
41 BEGIN_TEXT
42 $BR 43 Find the normalizing constant $$c$$ so that 44 $$\int_{-\infty}^{\infty}ce^{-x^2/sigma} \, dx = 1$$. 45$BR
46 $$c =$$ \{ans_rule(20)\}
47 $PAR 48 END_TEXT 49$pi = acos(-1);
50     ANS(num_cmp(1/sqrt($pi*$sigma)));
51
52 ENDDOCUMENT();
53
54
55
56