View of /trunk/NationalProblemLibrary/Rochester/setIntegrals19Area/sc6_1_14.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('integration','graph','area','trigonometric')
    6 ## Tagged by cmd6a 4/26/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Integration')
   10 ## DBsection('Areas Between Curves')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 ## TitleText2('Calculus: Early Transcendentals')
   20 ## EditionText2('1')
   21 ## AuthorText2('Rogawski')
   22 ## Section2('6.1')
   23 ## Problem2('45')
   24 
   25 DOCUMENT();        # This should be the first executable line in the problem.
   26 
   27 loadMacros(
   28 "PG.pl",
   29 "PGbasicmacros.pl",
   30 "PGchoicemacros.pl",
   31 "PGanswermacros.pl",
   32 "PGauxiliaryFunctions.pl"
   33 );
   34 
   35 TEXT(beginproblem());
   36 $showPartialCorrectAnswers = 1;
   37 
   38 $a=random(2, 9);
   39 $b=random(3, 9);
   40 $soln = 2*($b**2-$a/sqrt(2));
   41 
   42 TEXT(EV2(<<EOT));
   43 Sketch the region enclosed by the given curves.
   44 Decide whether to integrate with respect to x or y.
   45 Then find the area of the region.
   46 $BR \( y = $a \cos x, \ \ y = ($b \sec(x))^2,  \ \ x = -\pi / 4,  \ \ x = \pi / 4 \)
   47 $BR \{ans_rule(30) \}
   48 EOT
   49 ANS(num_cmp($soln));
   50 
   51 ENDDOCUMENT();        # This should be the last executable line in the problem.