Consider the following

Integral sqrt [ (dx/dt)^{2}+(dy/dt)^{2}] dt where t varies from 0 to 2n

dx/dt = 1-2 cos t

dy/dt = 2sin t

(1-2 cos t)^{2}+4sin^{2}t= 1-4cost + 4 cos ^{2 } t +4 sin ^{2 } t = 5 -4 cost

Integral √(5-cos t) dt between 0 to 2n

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