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## Homework Statement

Evaluate the length of the spiral with parametric equation ψ(t) =< 2 cost, 2 sin t, π/t >, with t ∈ [0, 2π].

## Homework Equations

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

dS= √(dx/dt)

^{2}+(dy/dt)

^{2}

∫ 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.