Consider the region bounded by $y=\sqrt[\phantom{2}]{4x}$ and $y=2x.$ Set up $($but do not solve$)$ integrals to find:

$($a$)$ The volume of the solid generated by rotating this region about the x $-$axis using washers.

$($b$)$ The volume of the solid generated by rotating this region about the horizontal line $y=3$ using shells.

$(15$ points$)$