View of /trunk/NationalProblemLibrary/Union/setIntTrigonometric/an8_3_05.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('05')
   19 ## TitleText2('Calculus: Early Transcendentals')
   20 ## EditionText2('1')
   21 ## AuthorText2('Rogawski')
   22 ## Section2('7.3')
   23 ## Problem2('45')
   24 
   25 DOCUMENT();        # This should be the first executable line in the problem.
   26 
   27 loadMacros(
   28   "PGstandard.pl",
   29   "PGunion.pl",            # Union College utilities
   30   "MathObjects.pl",
   31   "PGcourse.pl",           # Customization file for the course
   32 );
   33 
   34 TEXT(beginproblem());
   35 
   36 ###################################
   37 # Setup
   38 
   39 $a = random(2,8,1);
   40 
   41 $integrand=Formula(" sin^{5}($a x)  ");
   42 
   43 ###################################
   44 # Main text
   45 
   46 Context()->texStrings;
   47 BEGIN_TEXT
   48 Evaluate the indefinite integral.
   49 $PAR
   50 \( \displaystyle\int $integrand \, dx \)
   51              = \{ans_rule(50)\} \( + C\).
   52 END_TEXT
   53 Context()->normalStrings;
   54 
   55 ###################################
   56 # Answers
   57 
   58 $showPartialCorrectAnswers = 1;
   59 Context()->flags->set(reduceConstants=>0);
   60 
   61 $antideriv = Formula(  "-(1/$a)*[cos($a x)-(2/3)*(cos(${a}x))^3+(1/5)*(cos(${a}x))^5]")
   62                     ->with(limits => [0,5]);
   63 
   64 ANS($antideriv->cmp(upToConstant=>1));
   65 
   66 ###################################
   67 
   68 
   69 COMMENT('MathObject version');
   70 ENDDOCUMENT();