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| 1 : | apizer | 1647 | ## 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 : | |||
| 15 : | loadMacros( | ||
| 16 : | "PG.pl", | ||
| 17 : | "PGbasicmacros.pl", | ||
| 18 : | "PGchoicemacros.pl", | ||
| 19 : | "PGanswermacros.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(); |
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