View of /trunk/NationalProblemLibrary/Union/setIntTrigonometric/an8_3_06.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('06')
   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 $n = random(3,9,1);
   35 
   36 $integrand=Formula(" tan^{$n}(x) sec^{2}(x)  ");
   37 
   38 ###################################
   39 # Main text
   40 
   41 Context()->texStrings;
   42 BEGIN_TEXT
   43 Evaluate the indefinite integral.
   44 $PAR
   45 \( \displaystyle\int $integrand \, dx \)
   46              = \{ans_rule(50)\} \( + C\).
   47 END_TEXT
   48 Context()->normalStrings;
   49 
   50 ###################################
   51 # Answers
   52 
   53 $showPartialCorrectAnswers = 1;
   54 Context()->flags->set(reduceConstants=>0);
   55 
   56 $power = $n+1;
   57 $antideriv = Formula(  "(1/$power)(tan^{$power}(x))")
   58                     ->with(limits => [0,1]);
   59 
   60 ANS($antideriv->cmp(upToConstant=>1));
   61 
   62 ###################################
   63 
   64 
   65 COMMENT('MathObject version');
   66 ENDDOCUMENT();