View of /trunk/NationalProblemLibrary/Union/setIntByParts/sc5_6_01.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus','integration','integration by parts')
    6 ## Tagged by cmd6a 8/9/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Techniques of Integration')
   10 ## DBsection('Integration by Parts')
   11 ## Date('10/8/03')
   12 ## Author('K. Lesh')
   13 ## Institution('Union College')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23    "PG.pl",
   24    "PGbasicmacros.pl",
   25    "PGchoicemacros.pl",
   26    "PGanswermacros.pl",
   27    "PGauxiliaryFunctions.pl",
   28    "PGunion.pl",        # Union College utilities
   29    "PGcourse.pl",       # Customization file for the course
   30 );
   31 
   32 TEXT(beginproblem());
   33 BEGIN_PROBLEM();
   34 
   35 $a = random(2,4,1);
   36 $coeff = 1 / $a;
   37 $antiderv = "$coeff(x e^(${a}x) - ${coeff}e^(${a}x))";
   38 
   39 BEGIN_TEXT
   40 Evaluate the indefinite integral.
   41 $PAR
   42 \( \displaystyle\int x e^{$a x} \;dx \)
   43              = \{ans_rule(45)\} \( + C\).
   44 END_TEXT
   45 
   46 ##set $PG_environment{'textbook'} in webworkCourse.ph
   47 if (defined($textbook)) {
   48    if ($textbook eq "EllisGulick5") {
   49 BEGIN_TEXT
   50 $PAR
   51 This is similar to problem 8 of section 7.1 in the text.
   52 END_TEXT
   53 }
   54 }
   55 
   56 $showPartialCorrectAnswers = 1;
   57 
   58 ANS(fun_cmp($antiderv, mode=>"antider", vars=>"x", limits=>[0,1]));
   59 
   60 END_PROBLEM();
   61 ENDDOCUMENT();