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Homework Help: Rewrite curve as arclength function

  1. Oct 7, 2013 #1
    1. The problem statement, all variables and given/known data
    Consider the curve r = <cos(3t)e^(3t),sin(3t)e^(3t),e^(3t)>
    compute the arclength function s(t) with the initial point t = 0.

    2. Relevant equations
    s = integral |r'(t)|dt

    3. The attempt at a solution
    Okay so if you work all of this out it turns out it's not as bad as it looks.. it's set up to come out really nicely it appears. I end up with

    s = 3^(1/2)e^(3t)

    but my online homework program is saying that this is wrong... Do I ever use the information that the initial point is t = 0? I don't understand why they need to tell me that...
  2. jcsd
  3. Oct 7, 2013 #2


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    Science Advisor
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    Gold Member

    When you put ##t=0## you aren't getting ##s(0)=0## like the problem asks. You need to calculate$$
    s(t) - s(0) = \int_0^t|r'(t)|dt$$with s(0)=0. I'm guessing you didn't handle the lower limit correctly.
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