View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S2/problem_4.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 Regions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Basic Multivariable Calculus')
   15 ## EditionText1('')
   16 ## AuthorText1('Marsden, Tromba, and Weinstein')
   17 ## Section1('5.3')
   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(1, 5, 1);
   41 $b = random(1, 5, 1);
   42 $c = 2*$a;
   43 $c_x = clean_scalar_string($c,"x");
   44 $d = 2*$b;
   45 $d_y = clean_scalar_string($d,"y");
   46 $e = 4*$a*$b;
   47 
   48 BEGIN_TEXT
   49 Calculate the double integral
   50 \( \int \int_{\mathbf{R}} ($c_x + $d_y + $e )\: dA \)
   51 where \( \mathbf{R} \) is the region:
   52 \( 0 \leq x \leq $b, 0 \leq y \leq $a \).
   53 $PAR
   54 \{ ans_rule(40) \}
   55 END_TEXT
   56 
   57 ANS(num_cmp( 6 * $a**2 * $b**2 ) );
   58 
   59 
   60 
   61 ENDDOCUMENT();
   62 
   63 
   64 
   65