View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S3/ur_vc_8_12.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('double integral' 'order')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Multiple Integrals')
   10 ## DBsection('Double Integrals over General Regions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Basic Multivariable Calculus')
   15 ## EditionText1('3')
   16 ## AuthorText1('Marsden, Tromba, Weinstein')
   17 ## Section1('5.3')
   18 ## Problem1('')
   19 
   20 
   21 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 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(1, 9, 1);
   34 
   35 BEGIN_TEXT
   36 Evaluate the integral by reversing the order of integration. $BR
   37 \( \int_{0}^{1}\!\!\int_{$a\!y}^{$a} e^{x^{2}} \: dx dy = \)
   38 \{ ans_rule(20) \}
   39 END_TEXT
   40 
   41 ANS(num_cmp( 1/(2*$a) * (exp(1) - 1) ) );
   42 
   43 ENDDOCUMENT();    # This should be the last executable line in the problem.