View of /trunk/NationalProblemLibrary/UCSB/Stewart5_7_4/Stewart5_7_4_39.pg

    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 
   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();