View of /branches/UGA/7.2.12.pg

    1 ## DESCRIPTION
    2 ## Multivariable Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus','triple integral')
    6 
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Multiple Integrals')
   10 ## DBsection('Triple Integrals')
   11 ## Date('December 23, 2009')
   12 ## Author('Ted Shifrin')
   13 ## Institution('UGA')
   14 ## TitleText1()
   15 
   16 
   17 DOCUMENT();
   18 loadMacros("PG.pl",
   19            "PGbasicmacros.pl",
   20            "PGchoicemacros.pl",
   21            "PGanswermacros.pl",
   22            "PGauxiliaryFunctions.pl",
   23            "Parser.pl",
   24            );
   25 
   26 
   27 $showPartialCorrectAnswers = 1;
   28 
   29 Context("Numeric")->variables->are(x=>'Real',y=>'Real',z=>'Real');
   30 
   31 $a = random(1,5);
   32 $b = random(1,3);
   33 
   34 
   35 $f = Formula("$a y")->reduce;
   36 $g = Formula("$b**2-x^2")->reduce;
   37 
   38 @fn = ("1","y","z");
   39 @choice = NchooseK($#fn,1);
   40 $h = Formula("@fn[@choice[0]]")->reduce;
   41 
   42 @ans=(Compute("8*$a*$b^5/15"),Compute("32*$a*$b^7/105"),Compute("16*$a^2*$b^7/105"));
   43 $ans=@ans[@choice[0]];
   44 
   45 TEXT(beginproblem());
   46 
   47 
   48 Context()->texStrings;
   49 BEGIN_TEXT
   50 
   51 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
   52 \[ \int_\Omega $h\,dV \ .\]
   53 
   54 $PAR
   55 
   56 
   57 $PAR
   58 \{ans_rule(10)\}
   59 
   60 
   61 END_TEXT
   62 
   63 ANS($ans->cmp);
   64 
   65 
   66 ENDDOCUMENT();