Question $4.$ marks$]$

$($a$)$ Suppose ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}4ydx+7xdy=13,$ where $C$ is a simple, smooth curve oriented counterclockwise in the $xy-$plane that encloses the region $R.$ Use Green's Theorem to find the area of $R.$

$($b$)$ Evaluate ${}_D{\displaystyle \underset{D}{\overset{\phantom{}}{}}}8xyzdV,$ where $D$ is the region bounded by the surface $y=x^2,$ the plane $y+z=9$ and the $xy-$plane.