Reparametrizing a Curve with Respect to Arc Length

[zhuyilun]

Homework Statement

reparametrize the curve r(t)=e^t*i+e^t*sin(t)*j+e^t*cost*k with respect to arc length measured from the point (1,0,1)in the direction of increasing t

Homework Equations

arc length= integral( r'(t) from a to b)

The Attempt at a Solution

i don't know how to start this question. somebody help

 

[LCKurtz]

Remember that the speed ds/dt is |r'(t)|. Your point (1,0,1) corresponds to t = 0 and is where you want to start measuring arc length.

So calculate |r'(t)| = ds/dt. You should then be able to figure out s in terms of t for your substitution. And don't forget t = 0 corresponds to s = 0.