Mathematics

Problem

Let

S

be the region in the first quadrant bounded by

y=\sin x

and

y=\cos x

for

0\le x\le \dfrac{\pi}{2}

. When

S

is revolved about the

x

-axis, what is the volume of the resulting solid? a)

2\pi(\sqrt{2}-1)

\dfrac{\pi}{2}

\dfrac{\pi^{2}}{2}

\pi