View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S2/problem_9.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('double integral' 'iterated integral')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Multiple Integrals')
   10 ## DBsection('The Double Integral over a Rectangle')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Basic Multivariable Calculus')
   15 ## EditionText1('')
   16 ## AuthorText1('Marsden, Tromba, and Weinstein')
   17 ## Section1('5.2')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 loadMacros("PG.pl",
   22            "PGbasicmacros.pl",
   23            "PGchoicemacros.pl",
   24            "PGanswermacros.pl",
   25            "PGauxiliaryFunctions.pl",
   26            "PGgraphmacros.pl",
   27            "Dartmouthmacros.pl");
   28 
   29 
   30 ## Do NOT show partial correct answers
   31 $showPartialCorrectAnswers = 1;
   32 
   33 ## Lots of set up goes here
   34 
   35 
   36 ## Ok, we are ready to begin the problem...
   37 ##
   38 TEXT(beginproblem());
   39 
   40 $a = random(-5, 5, 1);
   41 $b = random(1, 4, 1);
   42 $c = random(-5, 5, 1);
   43 $d = random(1, 4, 1);
   44 $e = random(-5, 5, 1);
   45 $f = random(-5, 5, 1);
   46 $g = $a + $b;
   47 $h = $c + $d;
   48 
   49 BEGIN_TEXT
   50 If \( \int_{$a}^{$g} f(x) \: dx = $e \) and
   51 \( \int_{$c}^{$h} g(x) \: dx = $f \), what is the value of
   52 \( \iint_{D} f(x) g(y) \: dA \) where \( D \)
   53 is the square: \( $a \leq x \leq $g, $c \leq y \leq $h \)?
   54 $PAR
   55 \{ ans_rule(20) \}
   56 END_TEXT
   57 
   58 ANS(num_cmp( $e*$f ) );
   59 
   60 
   61 
   62 ENDDOCUMENT();
   63 
   64 
   65 
   66