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Thu Jul 19 21:11:19 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1187 byte(s)
Updated/Consolidated tags.


    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('Double Integrals over Rectangles')
11 ## Date('')
12 ## Author('')
13 ## Institution('Dartmouth')
14 ## TitleText1('Basic Multivariable Calculus')
15 ## EditionText1('3')
16 ## AuthorText1('Marsden, Tromba, 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 $showPartialCorrectAnswers = 1; 32 33 ## Lots of set up goes here 34$a = random(0,5,1);
35 $b = random($a+1,$a+6,1); 36$c = random(1,9,1);
37 $d = random($c+1,$c+6,1); 38 39 40 ## Ok, we are ready to begin the problem... 41 ## 42 TEXT(beginproblem()); 43 44 45 BEGIN_TEXT 46$BR
47     Find $$\int_{a}^{b} \int_{c}^{d}( x + \log y) \,dydx$$
48 $BR 49 50 \{ans_rule(60)\} 51$PAR
52 END_TEXT
53
54 $alpha =$d*(log($d) - 1) -$c*(log($c) - 1); 55$ans = ($d -$c)*($b**2 -$a**2)/2 + $alpha*($b - $a); 56 57 ANS(num_cmp($ans));
58 ENDDOCUMENT();
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