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# View of /trunk/NationalProblemLibrary/Union/setIntInverseTrigSub/an8_4_09.pg

Fri Aug 11 22:53:54 2006 UTC (6 years, 9 months ago) by jjholt
File size: 1047 byte(s)
Added tags.


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('calculus','integration','trig substitution')
6 ## Tagged by cmd6a 8/9/06
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Techniques of Integration')
10 ## DBsection('Trig Substitution')
11 ## Date('10/7/03')
12 ## Author('K. Lesh')
13 ## Institution('Union College')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();
22    "PG.pl",
23    "PGbasicmacros.pl",
24    "PGchoicemacros.pl",
26    "PGauxiliaryFunctions.pl",
27    "PGunion.pl",        # Union College utilities
28    "PGcourse.pl",       # Customization file for the course
29 );
30
31 TEXT(beginproblem());
32 BEGIN_PROBLEM();
33
34 $a = random(4,10,1); 35$aa = $a**2; 36 37$antiderv = "$a(x/$a - arctan(x/$a))"; 38 39 BEGIN_TEXT 40 Evaluate the indefinite integral. 41$PAR
42 $$\displaystyle\int \frac{x^2}{aa + x^2}\; dx$$
43              = \{ans_rule(50)\} $$+ C$$.
44 END_TEXT
45
46 $showPartialCorrectAnswers = 1; 47 ANS(fun_cmp($antiderv, mode=>"antider", vars=>"x", limits=>[0,1]));
48
49 END_PROBLEM();
50 ENDDOCUMENT();