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    1 ##KEYWORDS('integrals', 'integration by parts')
2 ##DESCRIPTION
3 ## Use integration by parts to evaluate a definite integral.
4 ##ENDDESCRIPTION
5
6 ## AmberHolden tagged
7 ## Shotwell cleaned
8
9 ## DBsubject('Calculus')
10 ## DBchapter('Techniques of Integration')
11 ## DBsection('Integration by Parts')
12 ## Date('6/3/2002')
13 ## Author('')
14 ## Institution('')
15 ## TitleText1('Calculus Early Transcendentals')
16 ## EditionText1('4')
17 ## AuthorText1('Stewart')
18 ## Section1('7.1')
19 ## Problem1('17,18')
20
21
22
23 DOCUMENT();        # This should be the first executable line in the problem.
24
26 "PGbasicmacros.pl",
28 "PGauxiliaryFunctions.pl"
29 );
30
31 TEXT(beginproblem());
32 $showPartialCorrectAnswers = 1; 33 34$a = random(1,4,1);
35 $l = random(3,6,1); 36 37$b = $a +$l;
38
39 $c = random(2,5,1); 40$n = random(2,4,1);
41 $m =$n + 1;
42
43 $soln = "($b^($m)/$m)*(ln($c*$b) - 1/$m) - ($a^($m)/$m)*(ln($c*$a) - 1/$m)"; 44 45 BEGIN_TEXT 46 Evaluate the definite integral. 47$BR$BR 48 $\int_{a}^{b} t^{n} \ln (c t) dt$ 49$BR
51 $BR 52 END_TEXT 53 54 ANS(num_cmp($soln));