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# View of /trunk/NationalProblemLibrary/Rochester/setIntegrals0Theory/sc5_2_2a.pg

Fri Apr 28 21:06:19 2006 UTC (7 years ago) by jjholt
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    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('integral' 'summation' 'area' 'riemann')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Integrals')
10 ## DBsection('Area and Distance')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
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 );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 1; 32 33$l= random(3, 5, 1);
34 $k= random(0,2,1); 35$lbound =-.5-$k; 36$ubound = $l+.5; 37$n = 1+$k+$l;
38
39 BEGIN_TEXT
40 Use the Midpoint Rule  to approximate $\int_{lbound}^{ubound} x^3 dx$
41   with $$n= n$$.$BR 42 \{ans_rule(40)\} 43 44 END_TEXT 45 46$ansA = .25*($l**4 + 2*$l**3 + $l**2 -$k**4 -2*$k**3 -$k**2);
47
48 ANS(num_cmp(\$ansA));
49
50 ENDDOCUMENT();        # This should be the last executable line in the problem.