## DESCRIPTION
## Calculus
## ENDDESCRIPTION

## KEYWORDS('arc length')
## Tagged by tda2d

## DBsubject('Calculus')
## DBchapter('Vector Functions')
## DBsection('Arc Length and Curvature')
## Date('')
## Author('')
## Institution('Dartmouth')
## TitleText1('Calculus')
## EditionText1('5')
## AuthorText1('Stewart')
## Section1('14.3')
## Problem1('')

DOCUMENT();
loadMacros("PG.pl",
           "PGbasicmacros.pl",
           "PGchoicemacros.pl",
           "PGanswermacros.pl",
           "PGauxiliaryFunctions.pl",
           "PGgraphmacros.pl",
           "Dartmouthmacros.pl");
 

## Do NOT show partial correct answers
$showPartialCorrectAnswers = 0;

$a = random(2,10);


## Ok, we are ready to begin the problem...
##
TEXT(beginproblem());


BEGIN_TEXT
$BR
Find the arclength of the curve
\(\mathbf r(t) =  \langle $a \sqrt2$SPACE t, e^{$a t}, e^{-$a t}\rangle\),
\(0 \le t \le 1\)
$BR
\{ans_rule()\}

$PAR
END_TEXT

    ANS(num_cmp(exp($a) - exp(- $a)));

ENDDOCUMENT();