## DESCRIPTION ## Calculus ## ENDDESCRIPTION ## KEYWORDS('double integral' 'iterated integral') ## Tagged by tda2d ## DBsubject('Calculus') ## DBchapter('Multiple Integrals') ## DBsection('Double Integrals over Rectangles') ## Date('') ## Author('') ## Institution('Dartmouth') ## TitleText1('Basic Multivariable Calculus') ## EditionText1('3') ## AuthorText1('Marsden, Tromba, Weinstein') ## Section1('5.2') ## Problem1('') DOCUMENT(); loadMacros("PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGgraphmacros.pl", "Dartmouthmacros.pl"); ## Do NOT show partial correct answers $showPartialCorrectAnswers = 1; ## Lots of set up goes here$a = random(0,5,1); $b = random($a+1,$a+6,1);$c = random(1,9,1); $d = random($c+1,$c+6,1); ## Ok, we are ready to begin the problem... ## TEXT(beginproblem()); BEGIN_TEXT$BR Find $$\int_{a}^{b} \int_{c}^{d}( x + \log y) \,dydx$$ $BR \{ans_rule(60)\}$PAR END_TEXT $alpha =$d*(log($d) - 1) -$c*(log($c) - 1);$ans = ($d -$c)*($b**2 -$a**2)/2 + $alpha*($b - $a); ANS(num_cmp($ans)); ENDDOCUMENT();