View of /trunk/NationalProblemLibrary/OSU/accelerated_calculus_and_analytic_geometry_i/hmwk8/prob5.pg

    1 ## DESCRIPTION
    2 ##   Integration by Parts
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Integration', 'Parts')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Techniques of Integration')
   10 ## DBsection('Integration by Parts')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('OSU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   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 $showPartialCorrectAnswers = 1;
   31 
   32 
   33 $a = random(1,7,1);
   34 $e = exp(1);
   35 $ans = "-$a * $e^(-$a) - $e^(-$a) + 1";
   36 
   37 TEXT(beginproblem());
   38 BEGIN_TEXT
   39 
   40 Use integration by parts to evaluate the definite integral.
   41 $BR \[ \int_{0}^{$a} t e^{-t} dt \]
   42 $BR $BR \{ans_rule( 60) \}
   43 $PAR
   44 
   45 This is similar to problem 29 in section 7.1 of the text.
   46 END_TEXT
   47 
   48 ANS(num_cmp($ans));
   49 
   50 ENDDOCUMENT();