Mathematics

Problem

Region R is enclosed by the curves

x=y^{2}

and

x=4-y^{2}

for

-2\le y\le 2

. A solid S has base R and square cross sections perpendicular to the y-axis. Which of the following expressions represents the volume of S? a)

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

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

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

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