Mathematics

Problem

Let

S

be the region enclosed by the graphs of

y=\sin x

and

y=1-\sin x

on the interval

[-\tfrac{\pi}{2},\tfrac{\pi}{2}]

. Which of the following represents the exact area of

S

? a)

\dfrac{2\pi}{3}+2

\dfrac{\pi}{3}+2\sqrt{3}

\pi

\dfrac{\pi}{3}+\sqrt{3}