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Revision 269 - (view) (download)
| 1 : | jjholt | 156 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 134 | |
| 5 : | jjholt | 156 | ## 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 : | jj | 134 | DOCUMENT(); |
| 21 : | loadMacros("PG.pl", | ||
| 22 : | "PGbasicmacros.pl", | ||
| 23 : | "PGchoicemacros.pl", | ||
| 24 : | "PGanswermacros.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 - $a); | ||
| 56 : | |||
| 57 : | gage | 269 | ANS(num_cmp($ans)); |
| 58 : | jj | 134 | ENDDOCUMENT(); |
| 59 : | |||
| 60 : | |||
| 61 : | |||
| 62 : |
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