View of /trunk/NationalProblemLibrary/Rochester/setIntegrals21Length/S08.01.ArcLength.PTP23.pg

    1 ##KEYWORDS('Integrals', 'Arc Length')
    2 ##DESCRIPTION
    3 ## Find the length of a given curve.
    4 ##ENDDESCRIPTION
    5 
    6 ## Shotwell cleaned
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Integration')
   10 ## DBsection('Arc Length')
   11 ## Date('6/3/2007')
   12 ## Author('Paul Pearson')
   13 ## Institution('University of Rochester')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('8.1')
   18 ## Problem1('')
   19 
   20 
   21 #DESCRIPTION
   22 #  Integration
   23 #  Arc length
   24 #ENDDESCRIPTION
   25 
   26 #KEYWORDS('Integration', 'Physics', 'Applications')
   27 
   28 DOCUMENT();        # This should be the first executable line in the problem.
   29 
   30 loadMacros(
   31 "PG.pl",
   32 "PGbasicmacros.pl",
   33 "PGchoicemacros.pl",
   34 "PGanswermacros.pl",
   35 "PGauxiliaryFunctions.pl"
   36 );
   37 
   38 TEXT(beginproblem());
   39 $showPartialCorrectAnswers = 1;
   40 
   41 
   42 $b = random(0.5,1.5,0.1);
   43 
   44 BEGIN_TEXT
   45 
   46 What is the length of the curve \( \ln(\sec(x)) \) from \(x = 0\) to \( x = $b \)?
   47 $BR
   48 
   49 \{ ans_rule(40) \}
   50 
   51 END_TEXT
   52 
   53 $answer = ln(sec($b) + tan($b));
   54 
   55 ANS(num_cmp($answer));
   56 
   57 ENDDOCUMENT();        # This should be the last executable line in the problem.