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    1 ## DESCRIPTION
    2 ## Antiderivative with Initial Condition
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus', 'antiderivative', 'integral', 'indefinite', 'initial condition')
    6 ## Tagged by YJ
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Differentiation')
   10 ## DBsection('Antiderivatives')
   11 ## Date('5/26/2005')
   12 ## Author('Jeff Holt')
   13 ## Institution('UVA')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('5e')
   16 ## AuthorText1('Stewart')
   17 ## Section1('4.10')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(20,80,10);
   34 $b = random(2,8,1);
   35 $c = random(2,8,1);
   36 
   37 TEXT(EV2(<<EOT));
   38 
   39 Find the particular antiderivative that satisfies the following conditions:
   40 $BR
   41 \[
   42  p'(x) = -\frac{$a}{x^2}; \quad p($b) = $c.
   43 \]
   44 $BR
   45 $BR
   46 \( p(x) = \) \{ans_rule(35) \}
   47 $BR
   48 
   49 EOT
   50 
   51 $ans = "($a/x) - ($a/$b) + $c";
   52 ANS(fun_cmp($ans, mode=>"antider", vars=>"x"));
   53 
   54 ENDDOCUMENT();