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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
23 "PGbasicmacros.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