Answer
$(2 \pi)\int_{-\pi/2}^{\pi/2} (\cos x) \sqrt {\sin^2 x +1} dx $
Work Step by Step
Our aim is to integrate the integral to compute the surface area. In order to solve the integral, we have:
$Surface \space Area(S_A)= (2 \pi)\int_{a}^{b} y \sqrt {1+(\dfrac{dy}{dx})^2}$
or, $ =(2 \pi)\int_{-\pi/2}^{\pi/2} (\cos x) \sqrt {\sin^2 x dx^2+dx^2} $
or, $ =(2 \pi)\int_{-\pi/2}^{\pi/2} (\cos x) \sqrt {\sin^2 x +1} dx $
