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

    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 
   22 loadMacros(
   23 "PGbasicmacros.pl",
   24 "PGanswermacros.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();