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# Annotation of /trunk/NationalProblemLibrary/UCSB/Stewart5_7_4/Stewart5_7_4_39.pg

 1 : apizer 1647 ## DBsubject('Calculus') 2 : ## DBchapter('Techniques of Integration') 3 : ## DBsection('Integration by Partial Fractions') 4 : ## KEYWORDS('integration', 'partial fractions') 5 : apizer 1674 ## TitleText1('Calculus: Early Transcendentals') 6 : ## EditionText1('5') 7 : apizer 1647 ## 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();