Mathematics

Problem

Consider the region bounded by

x=y^{2}

and

x=4

for

0\le y\le 2

. The region is revolved about the

y

-axis to generate a solid. Which of the following integrals equals the volume of this solid? a)

V=2\pi\displaystyle\int_{0}^{2} y\bigl(4-y^{2}\bigr)\,dy

V=\pi\displaystyle\int_{0}^{2}\bigl(16-y^{4}\bigr)\,dy

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

V=\pi\displaystyle\int_{0}^{2}\bigl(4-y^{2}\bigr)^{2}\,dy