View of /trunk/NationalProblemLibrary/Rochester/setIntegrals19Area/sc6_1_12.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('integrals', 'area between curvers')
    3 ## kshort tagged and PAID on 2-20-2004
    4 ## DBsubject('Calculus')
    5 ## DBchapter('Applications of Integration')
    6 ## DBsection('Areas Between Curves')
    7 ## Date('6/3/2002')
    8 ## Author('Arnie Pizer')
    9 ## Institution('rochester')
   10 ## TitleText1('Calculus: Early Transcendentals')
   11 ## EditionText1('6')
   12 ## AuthorText1('Stewart')
   13 ## Section1('6.1')
   14 ## Problem1('15,16,17,19')
   15 ## TitleText2('Calculus: Early Transcendentals')
   16 ## EditionText2('1')
   17 ## AuthorText2('Rogawski')
   18 ## Section2('6.1')
   19 ## Problem2('41')
   20 ##ENDDESCRIPTION
   21 
   22 DOCUMENT();        # This should be the first executable line in the problem.
   23 
   24 loadMacros(
   25 "PG.pl",
   26 "PGbasicmacros.pl",
   27 "PGchoicemacros.pl",
   28 "PGanswermacros.pl",
   29 "PGauxiliaryFunctions.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 
   35 $b=random(2, 8);
   36 $a= 1 - $b;
   37 $c= - $a * $b;
   38 
   39 $soln = $c * ($b - $a) + ($b**2 - $a**2)/2 - ($b**3 - $a**3)/3;
   40 
   41 
   42 BEGIN_TEXT
   43 
   44 Sketch the region enclosed by \( x + y^2 = $c\) and \( x + y = 0 \).
   45 Decide whether to integrate with respect to \(x\) or \(y\).
   46 Then find the area of the region.
   47 $BR \{ans_rule( 60) \}
   48 $BR
   49 
   50 END_TEXT
   51 
   52 ANS(num_cmp($soln));
   53 
   54 ENDDOCUMENT();        # This should be the last executable line in the problem.