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# View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S3/ur_vc_8_12.pg

Thu Jul 19 21:11:19 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1046 byte(s)
Updated/Consolidated tags.


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('double integral' 'order')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Multiple Integrals')
10 ## DBsection('Double Integrals over General Regions')
11 ## Date('')
12 ## Author('')
13 ## Institution('Dartmouth')
14 ## TitleText1('Basic Multivariable Calculus')
15 ## EditionText1('3')
16 ## AuthorText1('Marsden, Tromba, Weinstein')
17 ## Section1('5.3')
18 ## Problem1('')
19
20
21 DOCUMENT();   # This should be the first executable line in the problem.
22
24            "PGbasicmacros.pl",
25            "PGchoicemacros.pl",
31 $showPartialCorrectAnswers = 1; 32 33$a = random(1, 9, 1);
36 Evaluate the integral by reversing the order of integration. $BR 37 $$\int_{0}^{1}\!\!\int_{a\!y}^{a} e^{x^{2}} \: dx dy =$$ 38 \{ ans_rule(20) \} 39 END_TEXT 40 41 ANS(num_cmp( 1/(2*$a) * (exp(1) - 1) ) );