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# View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S2/problem_4.pg

Sat Jun 3 14:39:59 2006 UTC (6 years, 11 months ago) by gage
File size: 1259 byte(s)
 Cleaned problem code using convert-functions.pl


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('double integral' 'iterated integral')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Multiple Integrals')
10 ## DBsection('The Double Integral over Regions')
11 ## Date('')
12 ## Author('')
13 ## Institution('Dartmouth')
14 ## TitleText1('Basic Multivariable Calculus')
15 ## EditionText1('')
16 ## AuthorText1('Marsden, Tromba, and Weinstein')
17 ## Section1('5.3')
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 $showPartialCorrectAnswers = 1; 32 33 ## Lots of set up goes here 34 35 36 ## Ok, we are ready to begin the problem... 37 ## 38 TEXT(beginproblem()); 39 40$a = random(1, 5, 1);
41 $b = random(1, 5, 1); 42$c = 2*$a; 43$c_x = clean_scalar_string($c,"x"); 44$d = 2*$b; 45$d_y = clean_scalar_string($d,"y"); 46$e = 4*$a*$b;
47
48 BEGIN_TEXT
49 Calculate the double integral
50 $$\int \int_{\mathbf{R}} (c_x + d_y + e )\: dA$$
51 where $$\mathbf{R}$$ is the region:
52 $$0 \leq x \leq b, 0 \leq y \leq a$$.
53 $PAR 54 \{ ans_rule(40) \} 55 END_TEXT 56 57 ANS(num_cmp( 6 *$a**2 * \$b**2 ) );
58
59
60
61 ENDDOCUMENT();
62
63
64
65