Answer
$2 \pi \int_{-\pi/2}^{\pi/2} \cos (x) [\sqrt {\sin^2 x +1}] dx $
Work Step by Step
The formula to determine the surface area is as follows:
$S= \int_{m}^{n} 2 \pi y \sqrt {1+(\dfrac{dy}{dx})^2} \\ =(2 \pi)\int_{-\pi/2}^{\pi/2} (\cos x) \sqrt {\sin^2 x dx^2+dx^2} \\ =2 \pi \int_{-\pi/2}^{\pi/2} \cos (x) [\sqrt {\sin^2 x +1}] dx $
