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# View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S2/problem_9.pg

Sat Jun 3 14:39:59 2006 UTC (6 years, 11 months ago) by gage
File size: 1307 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 a Rectangle')
11 ## Date('')
12 ## Author('')
13 ## Institution('Dartmouth')
14 ## TitleText1('Basic Multivariable Calculus')
15 ## EditionText1('')
16 ## AuthorText1('Marsden, Tromba, and Weinstein')
17 ## Section1('5.2')
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(-5, 5, 1);
41 $b = random(1, 4, 1); 42$c = random(-5, 5, 1);
43 $d = random(1, 4, 1); 44$e = random(-5, 5, 1);
45 $f = random(-5, 5, 1); 46$g = $a +$b;
47 $h =$c + $d; 48 49 BEGIN_TEXT 50 If $$\int_{a}^{g} f(x) \: dx = e$$ and 51 $$\int_{c}^{h} g(x) \: dx = f$$, what is the value of 52 $$\iint_{D} f(x) g(y) \: dA$$ where $$D$$ 53 is the square: $$a \leq x \leq g, c \leq y \leq h$$? 54$PAR
55 \{ ans_rule(20) \}
56 END_TEXT
57
58 ANS(num_cmp( $e*$f ) );
59
60
61
62 ENDDOCUMENT();
63
64
65
66