Mathematics

Problem

The region bounded by

y=\sin x

and

y=\cos x

for

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

is revolved about the

x

-axis. Which of the following definite integrals equals the volume of the solid generated? a)

\displaystyle \pi\int_{0}^{\pi/2}(\cos x-\sin x)^{2}\,dx

\displaystyle \pi\int_{0}^{\pi/2}\bigl(\sin^{2}x+\cos^{2}x\bigr)\,dx

\displaystyle \pi\int_{0}^{\pi/4}\bigl(\cos^{2}x-\sin^{2}x\bigr)\,dx+\pi\int_{\pi/4}^{\pi/2}\bigl(\sin^{2}x-\cos^{2}x\bigr)\,dx

\displaystyle \pi\int_{0}^{\pi/2}\bigl(\cos^{2}x-\sin^{2}x\bigr)\,dx