Use cylindrical shells to find the volume of the solid that results when the region…

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

Problem

5. Use cylindrical shells to find the volume of the solid that results when the region between

x^{2}+y^{3}=4

x=0, x=4

, and

y=0

is revolved about the

y

-axis. Set up but do not evaluate the integral. (A)

\quad 2 \pi \int_{0}^{2} x\left(4-x^{2}\right)^{\frac{1}{3}} d x-2 \pi \int_{2}^{4} x\left(4-x^{2}\right)^{\frac{1}{3}} d x

(B)

\quad 2 \pi \int_{0}^{2} x\left(4-x^{2}\right)^{\frac{1}{3}} d x+2 \pi \int_{2}^{4} x\left(4-x^{2}\right)^{\frac{1}{3}} d x

(C)

\pi \int_{0}^{2}\left(4-x^{2}\right)^{\frac{2}{3}} d x-\pi \int_{2}^{4}\left(4-x^{2}\right)^{\frac{2}{3}} d x

(D)

\pi \int_{0}^{2}\left(4-x^{2}\right)^{\frac{2}{3}} d x+\pi \int_{2}^{4}\left(4-x^{2}\right)^{\frac{2}{3}} d x