$[6$ points$]$ Suppose that the following integral utilizing Shell Method was used $to$ calculate the

volume $of$ a solid obtained $by$ rotating a region $R$ about some axis $of$ revolution:

$2{\displaystyle \underset{a}{\overset{b}{}}}r(y)h(y)dy=2{\displaystyle \underset{0}{\overset{1}{}}}(y+3)(\sqrt[3]{y}-y^2)dy$

where $x=r(y)$ represents the radius $of$ a cylindrical shell and $x=h(y)$ represents the height

$of$ a cylindrical shell.

Determine the functions that bound the region $R$ and determine the axis $of$ revolution. Set $up$

$an$ integral that calculates the same volume $as$ the above integral, but uses Washer Method

instead.