Consider the following

The length of the curve equals ∫_{0}^{2π} √( (x'_{t})^{2} + (y'_{t})^{2}) dt = ∫_{0}^{2π} √( (1 – 2cos t )^{2} + (2sin t)^{2}) dt =

∫_{0}^{2π} √( 1 – 4cos t + 4cos^{2 }t + 4sin^{2 }t) dt = ∫_{0}^{2π} √( 5 – 4cos t) dt

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