View of /branches/CMA/set8.5_Representation_of_Periodic_Functions/pj25.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus','integration','definite')
    6 ## Tagged by cmd6a 8/9/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Integrals')
   10 ## DBsection('The Definite Integral')
   11 ## Date('8/23/07')
   12 ## Author('')
   13 ## Institution('')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23   "PGstandard.pl",
   24   "PGunion.pl",            # Union College utilities
   25   "MathObjects.pl",
   26   "PGcourse.pl",           # Customization file for the course
   27 );
   28 
   29 TEXT(beginproblem());
   30 
   31 ###################################
   32 # Setup
   33 
   34 $a = random(2,10,2);
   35 
   36 $upperdisplay= Formula("pi");
   37 $lowerdisplay= -Formula("pi");
   38 $upper=Real($upperdisplay->eval(x=>0));
   39 $lower=Real($lowerdisplay->eval(x=>0));
   40 
   41 $integrand=Formula("cos^2 ($a*x)");
   42 
   43 ###################################
   44 # Main text
   45 
   46 Context()->texStrings;
   47 BEGIN_TEXT
   48 Evaluate the definite integral.
   49 $PAR
   50 \( \displaystyle\int_{-\pi}^{\,\pi} $integrand \,dx \)
   51              = \{ans_rule(50)\}
   52 END_TEXT
   53 Context()->normalStrings;
   54 
   55 ###################################
   56 # Answers
   57 
   58 $showPartialCorrectAnswers = 1;
   59 Context()->flags->set(reduceConstants=>0);
   60 
   61 ANS(num_cmp( "pi" ) );
   62 
   63 ###################################
   64 
   65 
   66 COMMENT('MathObject version');
   67 ENDDOCUMENT();