The base of a solid is the region bounded by the graphs of $x=y^2$ and $x=4$. Cross sections perpendicular to the $y$-axis are squares. What is the volume of the solid?

Core Concept

Each square has side $4-y^2$, so its area is $(4-y^2)^2$. The volume is $\int_{-2}^2(4-y^2)^2\,dy=[16y-\frac{8y^3}{3}+\frac{y^5}{5}]_{-2}^2=\frac{512}{15}$.