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| 1 : | jjholt | 156 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 134 | |
| 5 : | jjholt | 156 | ## KEYWORDS('double integral' 'iterated integral') |
| 6 : | ## Tagged by tda2d | ||
| 7 : | jj | 134 | |
| 8 : | jjholt | 156 | ## DBsubject('Calculus') |
| 9 : | ## DBchapter('Multiple Integrals') | ||
| 10 : | jjholt | 483 | ## DBsection('Double Integrals over General Regions') |
| 11 : | jjholt | 156 | ## Date('') |
| 12 : | ## Author('') | ||
| 13 : | ## Institution('Dartmouth') | ||
| 14 : | ## TitleText1('Basic Multivariable Calculus') | ||
| 15 : | jjholt | 456 | ## EditionText1('3') |
| 16 : | jjholt | 443 | ## AuthorText1('Marsden, Tromba, Weinstein') |
| 17 : | jjholt | 156 | ## Section1('5.3') |
| 18 : | ## Problem1('') | ||
| 19 : | jj | 134 | |
| 20 : | jjholt | 156 | |
| 21 : | jj | 134 | DOCUMENT(); # This should be the first executable line in the problem. |
| 22 : | |||
| 23 : | loadMacros("PG.pl", | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGchoicemacros.pl", | ||
| 26 : | "PGanswermacros.pl", | ||
| 27 : | "PGauxiliaryFunctions.pl" | ||
| 28 : | ); | ||
| 29 : | |||
| 30 : | gage | 269 | TEXT(beginproblem()); |
| 31 : | jj | 134 | $showPartialCorrectAnswers = 1; |
| 32 : | |||
| 33 : | $a = random(1, 8, 1); | ||
| 34 : | $b = random(1, 8, 1); | ||
| 35 : | $a3 = 3*$a; | ||
| 36 : | $b2 = 2*$b; | ||
| 37 : | BEGIN_TEXT | ||
| 38 : | Evaluate the iterated integral | ||
| 39 : | \( I = \int_{0}^{1}\!\!\int_{1-x}^{1+x} ($a3\!x^{2} + $b2\!y )\: dy dx \) | ||
| 40 : | $PAR | ||
| 41 : | \{ ans_rule(40) \} | ||
| 42 : | END_TEXT | ||
| 43 : | |||
| 44 : | gage | 269 | ANS(num_cmp( $a*(3/2) + 2*$b ) ); |
| 45 : | jj | 134 | |
| 46 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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