View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh5S5/problem_2.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Gaussian' 'distribution' 'integral')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Integrals over Curves and Surfaces')
   10 ## DBsection('Line Integrals')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Basic Multivariable Calculus')
   15 ## EditionText1('')
   16 ## AuthorText1('Marsden, Tromba, Weinstein')
   17 ## Section1('6.1')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 loadMacros("PG.pl",
   22            "PGbasicmacros.pl",
   23            "PGchoicemacros.pl",
   24            "PGanswermacros.pl",
   25            "PGauxiliaryFunctions.pl",
   26            "PGgraphmacros.pl",
   27            "Dartmouthmacros.pl");
   28 
   29 
   30 ## Do NOT show partial correct answers
   31 $showPartialCorrectAnswers = 1;
   32 
   33 ## Lots of set up goes here
   34 $sigma = random(2,10,1);
   35 
   36 ## Ok, we are ready to begin the problem...
   37 ##
   38 TEXT(beginproblem());
   39 
   40 
   41 BEGIN_TEXT
   42 $BR
   43 Find the normalizing constant \( c \) so that
   44    \( \int_{-\infty}^{\infty}ce^{-x^2/$sigma} \, dx = 1\).
   45 $BR
   46 \( c = \) \{ans_rule(20)\}
   47 $PAR
   48 END_TEXT
   49     $pi = acos(-1);
   50     ANS(num_cmp(1/sqrt($pi*$sigma)));
   51 
   52 ENDDOCUMENT();
   53 
   54 
   55 
   56