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| 1 : | jjholt | 321 | ## 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 : | jj | 248 | 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(2,8,2); | ||
| 40 : | $c = random(5,13,2); | ||
| 41 : | $d = random(-6,-2,1); | ||
| 42 : | |||
| 43 : | BEGIN_TEXT | ||
| 44 : | Calculate the following antiderivatives: | ||
| 45 : | $PAR | ||
| 46 : | (a) \( \displaystyle\int x^{$a}\, dx \) = \{ans_rule\} \( + C\). | ||
| 47 : | $PAR | ||
| 48 : | (b) \( \displaystyle\int x^{$b/$c} \,dx \) = \{ans_rule\} \( + C\). | ||
| 49 : | $PAR | ||
| 50 : | (c) \( \displaystyle\int x^{$d}\sqrt{x} \,dx \) = \{ans_rule\} \( + C\). | ||
| 51 : | END_TEXT | ||
| 52 : | |||
| 53 : | $showPartialCorrectAnswers = 1; | ||
| 54 : | ########################## | ||
| 55 : | |||
| 56 : | $aa = $a + 1; | ||
| 57 : | $bb = $b + $c; | ||
| 58 : | $dd = $d + 1.5; | ||
| 59 : | ANS(fun_cmp("(1/$aa) x^($aa)", mode=>"antider")); | ||
| 60 : | ANS(fun_cmp("($c/$bb) x^($bb/$c)", mode=>"antider")); | ||
| 61 : | ANS(fun_cmp("(1/$dd) x^($dd)", mode=>"antider", vars=>"x", limits=>[1,2])); | ||
| 62 : | ############################################## | ||
| 63 : | |||
| 64 : | END_PROBLEM(); | ||
| 65 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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