## DESCRIPTION
## Multivariable Calculus
## ENDDESCRIPTION

## KEYWORDS('calculus','triple integral')


## DBsubject('Calculus')
## DBchapter('Multiple Integrals')
## DBsection('Triple Integrals')
## Date('December 23, 2009')
## Author('Ted Shifrin')
## Institution('UGA')
## TitleText1()


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

$showPartialCorrectAnswers = 1;

Context("Numeric")->variables->are(x=>'Real',y=>'Real',z=>'Real');

$a = random(1,5);
$b = random(1,3);


$f = Formula("$a y")->reduce;
$g = Formula("$b**2-x^2")->reduce;

@fn = ("1","y","z");
@choice = NchooseK($#fn,1);
$h = Formula("@fn[@choice[0]]")->reduce;

@ans=(Compute("8*$a*$b^5/15"),Compute("32*$a*$b^7/105"),Compute("16*$a^2*$b^7/105"));
$ans=@ans[@choice[0]];

TEXT(beginproblem());


Context()->texStrings;
BEGIN_TEXT

Let \(\Omega\subset\mathbb R^3\) be the region bounded below by the \(xy\)-plane, above by \(z=$f\), and on the sides by \(y=$g\). Evaluate the integral
\[ \int_\Omega $h\,dV \ .\]

$PAR


$PAR
\{ans_rule(10)\}


END_TEXT

ANS($ans->cmp);


ENDDOCUMENT();