View of /trunk/NationalProblemLibrary/Union/setIntBasic/an7_2_13.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus','integration','indefinite integral')
    6 ## Tagged by cmd6a 8/9/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Integrals')
   10 ## DBsection('Indefinite Integrals')
   11 ## Date('9/28/03')
   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 ##############################################
   36 ##    problem setup:
   37 
   38 $a = random(2,8,1);
   39 $b = random(3,8,1);
   40 $d = random(3,9,1);
   41 $c = random(-6,-2,1);
   42 $e = random(5,15,1);
   43 $f = random(2,15,1);
   44 $g = non_zero_random(-5,-2,1);
   45 $h = random(1,9,2);
   46 $j = random(2,7,.5);
   47 $k = non_zero_random(-10,10,2);
   48 $m = random(2,8,1);
   49 
   50 BEGIN_TEXT
   51 Calculate the following antiderivatives:
   52 $PAR
   53 (a) \( \displaystyle\int x($k + x^{$m}) \,dx\) = \{ans_rule(30)\} \( + C\).
   54 $PAR
   55 (b) \( \displaystyle\int \frac{$c x^{$d} + $e x^{$f}}{x^{$g}} \,dx \) = \{ans_rule(30)\} \( + C\).
   56 $PAR
   57 (c) \( \displaystyle\int ($a + x^{$b})^{2} \,dx\) = \{ans_rule(30)\} \( + C\).
   58 END_TEXT
   59 
   60 $showPartialCorrectAnswers = 1;
   61 
   62 $mm = $m+2;
   63 $aa = $a**2;
   64 $cross = 2*$a;
   65 $bb = $b + 1;
   66 $bB = 2*$b + 1;
   67 $dd = $d - $g + 1;
   68 $ff = $f - $g + 1;
   69 $hh = -$h + 4;
   70 ANS(fun_cmp("($k/2)x^2 + (1/$mm)x^$mm", mode=>"antider"));
   71 ANS(fun_cmp("($c/$dd)x ^($dd) + ($e/$ff)x ^($ff)", mode=>"antider"));
   72 ANS(fun_cmp("${aa}x + ($cross/$bb)x^($bb)+(1/$bB)x^{$bB}", mode=>"antider"));
   73 
   74 END_PROBLEM();
   75 ENDDOCUMENT();        # This should be the last executable line in the problem.