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# Annotation of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S1/problem_4.pg

 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 :