A region is enclosed by the graph of

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

Problem

y=\ln (x+1)

, the

x

-axis, and the vertical line

x=e^{2}-1

. When this region is revolved about the

y

-axis, which of the following definite integrals equals the volume of the resulting solid? (a)

\displaystyle 2\pi\int_{0}^{2}\bigl(e^{y}-1\bigr)\,dy

(b)

\displaystyle \pi\int_{0}^{2}\bigl(e^{y}\bigr)^{2}\,dy

(c)

\displaystyle \pi\int_{0}^{2}\bigl(e^{y}-1\bigr)^{2}\,dy

(d)

\displaystyle \pi\int_{0}^{e^{2}-1}\bigl(\ln (x+1)\bigr)^{2}\,dx