$[12$ points$]$ Consider the double integral

${}_{R}f(x,y)dA={\displaystyle \underset{0}{\overset{8}{}}}{\displaystyle \underset{\frac{x}{4}}{\overset{\sqrt[3]{x}}{}}}(4x+3y^2)dydx$

a$.$ Sketch the region of integration $R$ in the $xy-$plane.

b$.$ Express the integral with the order of integration reversed.

c$.$ Which integral you would prefer to evaluate and why?

$3.[12$ points$]$ Consider the solid below the surface $z=3x-2y$ and above the region in the $x-$y plane bounded by $y=0,y=x,$ and $x=3.$

a$.$ Sketch the region of integration $R$ in the xy plane needed to calculate the volume as a double integral.

b$.$ Express the volume as an integral $($evaluate on the next page$)$