The region bounded by and is revolved about the –axis

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

Problem

The region bounded by

y = x^{2}

and

y = 4

is revolved about the

x

–axis. Which of the following definite integrals represents the volume of the resulting solid? (a)

V=\pi\displaystyle\int_{-2}^{2}\left(16-x^{4}\right)\,dx

(b)

V=\pi\displaystyle\int_{0}^{2}\left(16-x^{4}\right)\,dx

(c)

V=\pi\displaystyle\int_{-2}^{2}\left(4-x^{2}\right)\,dx

(d)

V=2\pi\displaystyle\int_{0}^{4}\left(4-x^{2}\right)\,dx