The region bounded by and for is revolved about the line

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

Problem

The region bounded by

y=x^{2}

and

y=4

for

-2\le x\le2

is revolved about the line

y=6

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

V=\pi\displaystyle\int_{-2}^{2}\left[(6-4)^{2}-(6-x^{2})^{2}\right]dx

(b)

V=\pi\displaystyle\int_{-2}^{2}\left[(6-x^{2})^{2}-(6-4)^{2}\right]dx

(c)

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

(d)

V=\pi\displaystyle\int_{-2}^{2}\left[(6-x^{2})^{2}\right]dx