The equations x = t + sin t, y = 1 – cos t, 0≤t≤2pi, define a curve C parametrically from the origin O to A(2pi, 0), which is rotated completely about Ox to form a surface S.

Find the length of the curve from O to A.

As I did so far,

dx/dt = 1 + cos t and dy/dt = sin t

Curve length OA =

My answer is 0. Where I did wrong?

But its correct answer is 8. Please help me.