Mathematics

Problem

Which of the following gives the volume

V

of the solid generated when the region bounded above by

y=R(x)

and below by

y=r(x)

(where

R(x)\ge r(x)

for

a\le x\le b

) is revolved about the

x

-axis? a)

V=\displaystyle \int_{a}^{b} 2\pi R(x)\,dx

V=\displaystyle \int_{a}^{b} \pi\bigl(R(x)-r(x)\bigr)\,dx

V=\displaystyle \int_{a}^{b} \pi\bigl(R(x)^2-r(x)^2\bigr)\,dx

V=\displaystyle \int_{a}^{b} \pi\bigl(r(x)^2-R(x)^2\bigr)\,dx