Reparametrization to find arc length

[llooppii]

Homework Statement

Reparametrize the curve with respect to arc length measured from the point where t=0 in the direction of increasing t.

r(t) = [e^(2t)cos(2t)]i+2j+[e^(2t)sin(2t)]k

Homework Equations

i know that the derivative of the arc length with respect to t = magnitude of the derivative of r(t).

The Attempt at a Solution

I found the derivative and found the magnitude, but am basically lost as of there.

 

[lanedance]

start by finding the arc length as function of t

 

[icystrike]

Let s(t) be the arc length, and I'm sure Ur calculus textbook will have the formula of arc length..

 

[icystrike]

In fact you can easily "derive" the formula with pythagorus theorem and riemman sum in mind.