Mathematics

Problem

The region

R

is bounded by the graph of

y=\dfrac{1}{x+2}

, the

x

–axis, and the vertical lines

x=0

and

x=4

. Region

R

is revolved about the

y

–axis to generate a solid. Which of the following expressions gives the exact volume of the solid? a)

2\pi\displaystyle\int_{0}^{4}\left(\dfrac{x}{x+2}\right)^{2}\,dx

\pi\displaystyle\int_{0}^{4}\dfrac{x}{x+2}\,dx

2\pi\displaystyle\int_{0}^{4}\dfrac{x}{x+2}\,dx

\pi\displaystyle\int_{0}^{4}\left(\dfrac{1}{x+2}\right)^{2}\,dx