## 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();