##KEYWORDS('Integrals', 'Arc Length') ##DESCRIPTION ## Find the length of a given curve. ##ENDDESCRIPTION ## Shotwell cleaned ## DBsubject('Calculus') ## DBchapter('Applications of Integration') ## DBsection('Arc Length') ## Date('6/3/2007') ## Author('Paul Pearson') ## Institution('University of Rochester') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('5') ## AuthorText1('Stewart') ## Section1('8.1') ## Problem1('') #DESCRIPTION # Integration # Arc length #ENDDESCRIPTION #KEYWORDS('Integration', 'Physics', 'Applications') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$b = random(0.5,1.5,0.1); BEGIN_TEXT What is the length of the curve $$\ln(\sec(x))$$ from $$x = 0$$ to $$x = b$$? $BR \{ ans_rule(40) \} END_TEXT$answer = ln(sec($b) + tan($b)); ANS(num_cmp(\$answer)); ENDDOCUMENT(); # This should be the last executable line in the problem.