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**geton** 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 =$\displaystyle \int_{0}^{2\pi} [(1+cos t)^2 + sin^2t]^ \frac {1}{2}dt$

$\displaystyle =\int_{0}^{2\pi} (2+2cos t)^\frac{1}{2}dt$

$\displaystyle =\int_{0}^{2\pi}2 cos \frac{t}{2}dt$

My answer is 0. Where I did wrong?

But its correct answer is 8. Please help me.