## DESCRIPTION ## Calculus ## ENDDESCRIPTION ## KEYWORDS('curve' 'length') ## Tagged by tda2d ## DBsubject('Calculus') ## DBchapter('Vector Functions') ## DBsection('Arc Length and Curvature') ## Date('') ## Author('') ## Institution('Dartmouth') ## TitleText1('Basic Multivariable Calculus') ## EditionText1('3') ## AuthorText1('Marsden, Tromba, Weinstein') ## Section1('4.2') ## Problem1('') DOCUMENT(); loadMacros("PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGgraphmacros.pl", "Dartmouthmacros.pl"); ## Do NOT show partial correct answers $showPartialCorrectAnswers = 1; ## Lots of set up goes here$a = non_zero_random( -5, 5, 1 ); $a_t = clean_scalar_string($a, "t"); $b = non_zero_random( -5, 5, 1 );$b_sin_t = clean_scalar_string($b, "\sin t");$b_cos_t = clean_scalar_string($b, "\cos t");$c = random( -5, -1, 1 ); $d = random( 1, 5, 1 ); ## Ok, we are ready to begin the problem... ## TEXT(beginproblem()); BEGIN_TEXT$BR Find the length of the given curve: $BR $$\mathbf{r} \left( t \right) = \left( a_t, b_sin_t, b_cos_t \right)$$ where $$c \leq t \leq d$$.$PAR \{ans_rule(10)\} END_TEXT $ans = ($d - $c) * sqrt($a**2 + $b**2 ); ANS(num_cmp($ans)); ENDDOCUMENT();