View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S1/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('Double Integrals over Rectangles')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Basic Multivariable Calculus')
   15 ## EditionText1('3')
   16 ## AuthorText1('Marsden, Tromba, 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 $a = random(0,5,1);
   35 $b = random($a+1,$a+6,1);
   36 $c = random(1,9,1);
   37 $d = random($c+1,$c+6,1);
   38 
   39 
   40 ## Ok, we are ready to begin the problem...
   41 ##
   42 TEXT(beginproblem());
   43 
   44 
   45 BEGIN_TEXT
   46 $BR
   47     Find \( \int_{$a}^{$b} \int_{$c}^{$d}( x + \log y) \,dydx \)
   48 $BR
   49 
   50 \{ans_rule(60)\}
   51 $PAR
   52 END_TEXT
   53 
   54 $alpha = $d*(log($d) - 1) - $c*(log($c) - 1);
   55 $ans = ($d - $c)*($b**2 - $a**2)/2 + $alpha*($b - $a);
   56 
   57 ANS(num_cmp($ans));
   58 ENDDOCUMENT();
   59 
   60 
   61 
   62