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    1 ##KEYWORDS('integrals', 'improper')
    2 ##DESCRIPTION
    3 ## Determine if an improper integral converges and evaluate it.
    4 ##ENDDESCRIPTION
    5 
    6 ## Shotwell cleaned
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Techniques of Integration')
   10 ## DBsection('Improper Integrals')
   11 ## Date('6/3/2002')
   12 ## Author('')
   13 ## Institution('')
   14 ## TitleText1('Calculus Early Transcendentals')
   15 ## EditionText1('4')
   16 ## AuthorText1('Stewart')
   17 ## Section1('7.8')
   18 ## Problem1('33')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PGbasicmacros.pl",
   24 "PGanswermacros.pl",
   25 "PGauxiliaryFunctions.pl"
   26 );
   27 
   28 TEXT(beginproblem());
   29 $showPartialCorrectAnswers = 1;
   30 
   31 $a = -random(1,20,1);
   32 $b = random(1,20,1);
   33 $c = random(2,8,2);
   34 
   35 BEGIN_TEXT
   36 
   37 Determine whether the integral is divergent or convergent.
   38 If it is convergent, evaluate it. $BR$BR
   39 If it diverges to infinity, state your answer as $BITALIC inf $EITALIC .
   40 If it diverges to negative infinity, state your answer as $BITALIC -inf $EITALIC . If it diverges without being infinity or negative infinity, state your answer as $BITALIC div $EITALIC .
   41 
   42 $BR \[ \int_{$a}^{$b}  \frac{1}{x^{$c}} \, dx \]
   43 $BR Answer: \{ans_rule(40) \}
   44 $BR
   45 END_TEXT
   46 
   47 ANS(num_cmp('inf', strings=>['inf', '-inf', 'div']));
   48 
   49 
   50 ENDDOCUMENT();        # This should be the last executable line in the problem.
   51