# Rewrite curve as arclength function

1. Oct 7, 2013

### PsychonautQQ

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. Oct 7, 2013

### LCKurtz

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.