$($calculator$)$

Let $R$ be the region bounded by the graph of $y=lnx$ and the line $y=2x-3.$

$($a$)$ Find the area of $R.$

$($b$)$ Find the volume of the solid generated when $R$ is rotated about the horizontal line $y=-3.$

$($c$)$ Write, but do not evaluate, an expression involving one or more integrals that can be used to find the volume of the solid generated when $R$ is revolved about the $y-$axis.