View of /trunk/NationalProblemLibrary/Utah/Calculus_II/set10_Infinite_Series/set10_pr10.pg

    1 #DESCRIPTION
    2 # Calculation of integrals using power series.
    3 #ENDDESCRIPTION
    4 ## Author('Utah ww group')
    5 ## Institution('Univeristy of Utah')
    6 ## DBsubject('Calculus')
    7 ## DBchapter('Infinite Sequences and Series')
    8 ## DBsection('Taylor and MacLaurin Series')
    9 ## AuthorText1('Dale Varberg, Edwin J. Purcell, and Steve E. Rigdon')
   10 ## TitleText1('Calculus')
   11 ## EditionText1('9')
   12 ## Section1('Infinite Series')
   13 ## Problem1('')
   14 ## KEYWORDS('calculus')
   15 
   16 DOCUMENT();        # This should be the first executable line in the problem.
   17 
   18 loadMacros(
   19 "PG.pl",
   20 "PGbasicmacros.pl",
   21 "PGchoicemacros.pl",
   22 "PGanswermacros.pl",
   23 "PGauxiliaryFunctions.pl"
   24 );
   25 
   26 TEXT(beginproblem());
   27 $showPartialCorrectAnswers = 1;
   28 
   29 $a = random(0.6,0.8,0.01);
   30 $c = random(2,8,1);
   31 
   32 BEGIN_TEXT
   33 Assume that \( \sin(x) \) equals its Maclaurin series for all x. $BR
   34 Use the Maclaurin series for \( \sin($c x^2) \)
   35 to evaluate the integral
   36 \[ \int_0^{$a} \sin($c x^2) \  dx. \]
   37 
   38 Your answer will be an infinite series.  Use the first two terms to estimate its value.
   39 
   40 \{ans_rule(40)\}
   41 END_TEXT
   42 
   43 
   44 $soln1 = "$c * x^3 / 3 - $c^3 * x^7 / 42";
   45 $soln2 = $c * $a**3 / 3 - $c**3 * $a**7 / 42;
   46 
   47 
   48 ANS(num_cmp($soln2, relTol=>1E-7));
   49 
   50 ENDDOCUMENT();        # This should be the last executable line in the problem.