View of /trunk/rochester_problib/setIntegrals14Substitution/sc5_5_49.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('integrals', 'substitution')
    3 ##ENDDESCRIPTION
    4 
    5 ## Before doing anything, we must import the macro definitions on the next few lines.
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros(
   10 "PG.pl",
   11 "PGbasicmacros.pl",
   12 "PGchoicemacros.pl",
   13 "PGanswermacros.pl",
   14 "PGauxiliaryFunctions.pl"
   15 );
   16 
   17 TEXT(&beginproblem);
   18 $showPartialCorrectAnswers = 1;
   19 
   20 $a = random(1,4,1);
   21 $b = random(1,5,1);
   22 $c = random(3,7,1);
   23 $coeff = 1 / $b;
   24 $soln = $coeff * (ln(($b * $a) + $c) - ln($c));
   25 
   26 TEXT(EV2(<<EOT));
   27 
   28 Evaluate the definite integral.
   29 $BR \[ \int_{0}^{ $a } \frac{dx}{$b x + $c} \]
   30 $BR $BR \{ans_rule( 30) \}
   31 $BR
   32 EOT
   33 
   34 $ans = $soln;
   35 &ANS(std_num_cmp($ans));
   36 
   37 ENDDOCUMENT();        # This should be the last executable line in the problem.