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# Annotation of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S3/ur_vc_8_9.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 : 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.