View of /trunk/NationalProblemLibrary/Union/setIntTrigonometric/an8_3_03.pg

    1 ## DESCRIPTION
    2 ##   Evaluate a Trig Integral
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Indefinite', 'Trig Integral')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Techniques of Integration')
   10 ## DBsection('Trigonometric Integrals')
   11 ## Date('8/23/07')
   12 ## Author('K. Lesh')
   13 ## Institution('Union')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('7')
   16 ## AuthorText1('Anton')
   17 ## Section1('8.3')
   18 ## Problem1('03')
   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 $integrand=Formula(" cos^{4}(x)  ");
   35 
   36 ###################################
   37 # Main text
   38 
   39 Context()->texStrings;
   40 BEGIN_TEXT
   41 Evaluate the indefinite integral.
   42 $PAR
   43 \( \displaystyle\int $integrand \, dx \)
   44              = \{ans_rule(50)\} \( + C\).
   45 END_TEXT
   46 Context()->normalStrings;
   47 
   48 ###################################
   49 # Answers
   50 
   51 $showPartialCorrectAnswers = 1;
   52 Context()->flags->set(reduceConstants=>0);
   53 
   54 $antideriv = Formula( "(3/8)x+(1/4)(sin(2x))+(1/32)(sin(4x))")
   55                                  ->with(limits => [0,5]);
   56 
   57 ANS($antideriv->cmp(upToConstant=>1));
   58 
   59 ###################################
   60 
   61 ENDDOCUMENT();        # This should be the last executable line in the problem.