$(4$ points each$)$ Let $R$ be the region bounded by the curves $y=\frac{x}{2},$ the $x-$axis, and the line $x=2$ and let $f(x,y)=y.$

$($a$)$ Draw a sketch of $R.$

$($b$)$ Compute ${\displaystyle \underset{R}{\overset{\phantom{}}{}}}f(x,y)dA$ by describing $R$ as a Type $1$ region.

$($c$)$ Compute ${\displaystyle \underset{R}{\overset{\phantom{}}{}}}f(x,y)dA$ by describing $R$ as a Type $2$ region.