Mathematics

Problem

Region

S

is bounded by

x=y^{3}

x=8

, and

y=0

. When

S

is revolved about the

y

-axis, which of the following definite integrals correctly represents the resulting volume

V

? a)

V=\pi\displaystyle\int_{0}^{2} (8-y^{3})^{2}\,dy

V=2\pi\displaystyle\int_{0}^{2} y\,(8-y^{3})\,dy

V=\pi \displaystyle\int_{0}^{2} \bigl[8^{2}-(y^{3})^{2}\bigr] \,dy

V=\pi\displaystyle\int_{0}^{2} \bigl[8^{2}-y^{3}\bigr] \,dy