Rewrite curve as arclength function

  • #1
PsychonautQQ
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Homework Statement


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.


Homework Equations


s = integral |r'(t)|dt


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...
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
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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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