$(10$ points$)$ Consider the region bounded by $y=\sqrt[\phantom{2}]{4x+1},y=0,x=2,$ and $x=3.$

$($a$)$ Label each curve with its equations.

$($b$)$ Set up a definite integral to find the volume of the solid formed by rotating the region about the $x-$axis. $($Do not evaluate this definite integral.$)$

$($c$)$ Set up a definite integral to find the volume of the solid formed by rotating the region about the $y-$axis. $($Do not evaluate this definite integral.$)$