x = t − 2 sin t, y = 1 − 2 cos t, 0 ≤ t ≤ 6π

Question

Set up an integral that represents the length of the curve.

Answer 1

s = ∫[0,6π] √((dx/dt)^2 + (dy/dt)^2) dt
= ∫[0,6π] √((1-2cost)^2 + (2sint)^2) dt
= ∫[0,6π] √(1-4cost+4cos^2t + 4sin^2t) dt
= ∫[0,6π] √(5-4cost) dt

Answer 2

40