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Tue Feb 1 04:12:46 2011 UTC (2 years, 3 months ago) by apizer
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1 ## DBsubject('Calculus')
2 ## DBchapter('Techniques of Integration')
3 ## DBsection('Integration by Partial Fractions')
4 ## KEYWORDS('integration', 'partial fractions')
5 ## TitleText1('Calculus')
6 ## EditionText1('5e')
7 ## AuthorText1('Stewart')
8 ## Section1('7.4')
9 ## Problem1('39')
10 ## Author('')
11 ## Institution('UCSB')
12
13 DOCUMENT();
14
16 "PG.pl",
17 "PGbasicmacros.pl",
18 "PGchoicemacros.pl",
20 "PGauxiliaryFunctions.pl"
21 );
22
23 TEXT(&beginproblem);
24 $showPartialCorrectAnswers = 1; 25$a=random(1,10,1)*random(-1,1,2);
26 $b=random(1,10,1)*random(-1,1,2); 27$c=random(1,10,1)*random(-1,1,2);
28 $d=(-3)*$a;
29
30 BEGIN_TEXT
31
32 $PAR 33 Make a substitution to express the integrand as a rational function and then evaluate the integral 34 $\int {\frac{a}{x\sqrt{x+1}}}\, dx$ 35 36$PAR
37 Note: Use an upper-case "C" for the constant of integration.
38
39 $PAR 40 \{ans_rule(45)\} 41 42 END_TEXT 43 44 ANS(fun_cmp("$a*(ln(abs(sqrt(x+1)-1)/abs(sqrt(x+1)+1)))+C+c", var=>["x","C"], params=>["c"], limits=>[[1.1,10],[-10,10]]));
45
46 ENDDOCUMENT();