## DESCRIPTION
## Calculus
## ENDDESCRIPTION

## KEYWORDS('double integral' 'iterated integral')
## Tagged by tda2d

## DBsubject('Calculus')
## DBchapter('Multiple Integrals')
## DBsection('The Double Integral over Regions')
## Date('')
## Author('')
## Institution('Dartmouth')
## TitleText1('Basic Multivariable Calculus')
## EditionText1('')
## AuthorText1('Marsden, Tromba, and Weinstein')
## Section1('5.3')
## Problem1('')


DOCUMENT();		# This should be the first executable line in the problem.

loadMacros("PG.pl",      
           "PGbasicmacros.pl",
           "PGchoicemacros.pl",      
           "PGanswermacros.pl",
           "PGauxiliaryFunctions.pl"     
          );      

TEXT(&beginproblem);
$showPartialCorrectAnswers = 1;

$a = random(1, 8, 1);
$b = random(1, 8, 1);
$a3 = 3*$a;
$b2 = 2*$b;
BEGIN_TEXT
Evaluate the iterated integral 
\( I = \int_{0}^{1}\!\!\int_{1-x}^{1+x} ($a3\!x^{2} + $b2\!y )\: dy dx \)
$PAR
\{ ans_rule(40) \}
END_TEXT

ANS( num_cmp( $a*(3/2) + 2*$b ) );

ENDDOCUMENT();		# This should be the last executable line in the problem.