Find the length of the curve r(t)=<e^(t) , e^(t)sin(t) , e^(t)cos(t)> between points (1,0,1) and (e^(2pi) , 0 , e^(2pi))
Length of curve=∫(llv(t)ll Where the limits of integration are the distance between the given points.
The Attempt at a Solution
First, to know what my limits are. I would like to assume they're from 1 to e^(2pi), but something tells me I have to calculate the distance somehow. Would that distance be D=√(Δx^(2)+Δy^(2)+Δz^(2)). Is this correct?
That's the only part I'm confused on. The integral itself isn't so bad.