Let be the region in the first quadrant bounded by and for

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

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)

(b)

\dfrac{\pi}{2}

(c)

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

(d)

\pi