View of /trunk/NationalProblemLibrary/Union/setIntInverseTrigSub/an8_4_09.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus','integration','trig substitution')
    6 ## Tagged by cmd6a 8/9/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Techniques of Integration')
   10 ## DBsection('Trig Substitution')
   11 ## Date('10/7/03')
   12 ## Author('K. Lesh')
   13 ## Institution('Union College')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 loadMacros(
   22    "PG.pl",
   23    "PGbasicmacros.pl",
   24    "PGchoicemacros.pl",
   25    "PGanswermacros.pl",
   26    "PGauxiliaryFunctions.pl",
   27    "PGunion.pl",        # Union College utilities
   28    "PGcourse.pl",       # Customization file for the course
   29 );
   30 
   31 TEXT(beginproblem());
   32 BEGIN_PROBLEM();
   33 
   34 $a = random(4,10,1);
   35 $aa = $a**2;
   36 
   37 $antiderv = "$a(x/$a - arctan(x/$a))";
   38 
   39 BEGIN_TEXT
   40 Evaluate the indefinite integral.
   41 $PAR
   42 \( \displaystyle\int \frac{x^2}{$aa + x^2}\; dx  \)
   43              = \{ans_rule(50)\} \( + C\).
   44 END_TEXT
   45 
   46 $showPartialCorrectAnswers = 1;
   47 ANS(fun_cmp($antiderv, mode=>"antider", vars=>"x", limits=>[0,1]));
   48 
   49 END_PROBLEM();
   50 ENDDOCUMENT();