1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Computing The Arclength Function

  1. Nov 18, 2008 #1
    1. The problem statement, all variables and given/known data

    Consider the curve r = (e^−2 t cos(3 t), e^−2 t sin(3 t), e^−2 t) .

    Compute the arclength function s(t) : (with initial point t=0 ).

    3. The attempt at a solution

    r'(t) = <-2e^-2t*cos(3t) + e^-2t*-3sin(3t), -2e^-2t*sin(3t) + e^-2t*cos(3t), -2e^-2t>

    Then what, do I find the length of that derivative?
    Then take the integral of 0 to t?
    I dunno.
  2. jcsd
  3. Nov 18, 2008 #2
    Hi Withthemotive,

    A minor point: the e^(-2t)*cos(3t) term in your second component is missing a factor of 3. Also, be sure to use plenty of parentheses to remove any ambiguity in the future!

    That's right, but your derivative will need to be with respect to a dummy variable, say u:
    [tex]s(t) = \int_0^t ||\text{r}'(u)|| \, \text{du}[/tex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook