Which of the following definite integrals gives the volume of the solid obtained when…

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

Problem

Which of the following definite integrals gives the volume of the solid obtained when the region bounded by

y=2x

, the

x

-axis, and

x=1

is revolved about the line

y=-1

? (a)

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

(b)

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

(c)

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

(d)

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