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

Fri Aug 11 22:53:54 2006 UTC (6 years, 10 months ago) by jjholt
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Added tags.


    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
23    "PG.pl",
24    "PGbasicmacros.pl",
25    "PGchoicemacros.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.