View of /trunk/NationalProblemLibrary/ma123DB/set2/s7_1_17.pg

    1 ##KEYWORDS('integrals', 'integration by parts')
    2 ##DESCRIPTION
    3 ## Use integration by parts to evaluate a definite integral.
    4 ##ENDDESCRIPTION
    5 
    6 ## AmberHolden tagged
    7 ## Shotwell cleaned
    8 
    9 ## DBsubject('Calculus')
   10 ## DBchapter('Techniques of Integration')
   11 ## DBsection('Integration by Parts')
   12 ## Date('6/3/2002')
   13 ## Author('')
   14 ## Institution('')
   15 ## TitleText1('Calculus Early Transcendentals')
   16 ## EditionText1('4')
   17 ## AuthorText1('Stewart')
   18 ## Section1('7.1')
   19 ## Problem1('17,18')
   20 
   21 
   22 
   23 DOCUMENT();        # This should be the first executable line in the problem.
   24 
   25 loadMacros(
   26 "PGbasicmacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 $a = random(1,4,1);
   35 $l = random(3,6,1);
   36 
   37 $b = $a + $l;
   38 
   39 $c = random(2,5,1);
   40 $n = random(2,4,1);
   41 $m = $n + 1;
   42 
   43 $soln = "($b^($m)/$m)*(ln($c*$b) - 1/$m) - ($a^($m)/$m)*(ln($c*$a) - 1/$m)";
   44 
   45 BEGIN_TEXT
   46 Evaluate the definite integral.
   47 $BR$BR
   48 \[ \int_{$a}^{$b} t^{$n} \ln ($c t) dt \]
   49 $BR
   50 Answer: \{ans_rule(60) \}
   51 $BR
   52 END_TEXT
   53 
   54 ANS(num_cmp($soln));
   55 
   56 ENDDOCUMENT();        # This should be the last executable line in the problem.