Reparametrization to find arc lengthby llooppii Tags: calculus, parametric equations, reparametrization, vectors 

#1
Sep2111, 08:53 PM

P: 8

1. The problem statement, all variables and given/known data
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 2. Relevant equations i know that the derivative of the arc length with respect to t = magnitude of the derivative of r(t). 3. The attempt at a solution I found the derivative and found the magnitude, but am basically lost as of there. 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 



#2
Sep2111, 08:57 PM

HW Helper
P: 3,309

start by finding the arc length as function of t




#3
Sep2211, 05:17 AM

P: 439

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




#4
Sep2211, 05:25 AM

P: 439

Reparametrization to find arc length
In fact you can easily "derive" the formula with pythagorus theorem and riemman sum in mind.



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