Mathematics

Problem

The region bounded by

y=\ln x

and the

x

-axis for

1\le x\le e

is revolved about the horizontal line

y=-1

. Which of the following integrals correctly represents the volume of the solid? a)

V=\displaystyle 2\pi\int_{1}^{e}x(\ln x)\,dx

V=\displaystyle \pi\int_{1}^{e}\big[(\ln x+1)^{2}-1\big]\,dx

V=\displaystyle \pi\int_{1}^{e}(\ln x)^{2}\,dx

V=\displaystyle \pi\int_{1}^{e}(\ln x+1)^{2}\,dx