Evaluate the length of the spiral with parametric equation ψ(t) =< 2 cost, 2 sin t, π/t >, with t ∈ [0, 2π].
Line integral ∫C f(x,y) dS
The Attempt at a Solution
f(x,y) = z = π/t
∫C π/t dS
[0, 2π] are the lower and upper bounds of integration
∫ π/t √(dx/dt)2+(dy/dt)2 ; 0≤t≤2π
Just wanted to check I've set this problem up correctly. At first I thought dS = √(dx/dt)2+(dy/dt)2 + (dz/dt)2 and that I would just integrate that with respect to the boundaries. I don't think this is correct though. I don't really understand why though.