## 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();