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# View of /branches/CMA/set8.5_Representation_of_Periodic_Functions/jdl704.pg

Tue Jul 26 00:08:54 2011 UTC (22 months ago) by david smith
File size: 1176 byte(s)

    1 ##DESCRIPTION
2 ##ENDDESCRIPTION
3 ##KEYWORDS('integrals', 'theory', 'Riemann sums')
4
5 ## Shotwell cleaned
6 ## lcao , PAID on 11-24-2003
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Integrals')
10 ## DBsection('The Definite Integral')
11 ## Date('6/3/2002')
12 ## Author('')
13 ## Institution('')
14 ## TitleText1('Calculus: Early Transcendentals')
15 ## EditionText1('6')
16 ## AuthorText1('Stewart')
17 ## Section1('5.2')
18 ## Problem1('22')
19
20 DOCUMENT();
21
23 "PGbasicmacros.pl",
25 "PGauxiliaryFunctions.pl"
26 );
27
28 $showPartialCorrectAnswers = 1; 29 30$a = random(2,7,1);
31 $aa =$a*$a; 32$a2 = 2*$a; 33$a3 = 3*$a; 34 35 TEXT(beginproblem()); 36 37 BEGIN_TEXT 38 The following sum 39 $40 \sqrt{aa - \left(\frac{a}{n}\right)^2} \cdot \frac{a}{n} + 41 \sqrt{aa - \left(\frac{a2}{n}\right)^2} \cdot \frac{a}{n} + 42 \ldots + \sqrt{aa - \left(\frac{a n}{n}\right)^2} \cdot \frac{a}{n} 43$$BR
44 is a right Riemann sum with $$n$$ subintervals of equal length
45 for the definite integral
46 $\int_0^b f(x)\, dx$
47 where $$b$$ = \{ ans_rule()\}
48 $BR 49 and $$f(x)$$ = \{ ans_rule()\} 50$BR
51 END_TEXT
52
53 ANS(num_cmp($a)); 54 ANS(fun_cmp("sqrt($aa - x^2)"));
55
56 ENDDOCUMENT();