$1.$ Consider the region $\backslash ($ R $\backslash )$ bounded by the curves $\backslash ($ y$=1,$ y$=$x$^\{3\}\backslash ),$ and $\backslash ($ x$=4\backslash ).$

$($a$)(2$ points$)$ Sketch a graph of the region. $($You should attempt this problem on your own first, but you may use Desmos to verify your answer.$)$

$($b$)(2$ points$)$ Compute the area of the region $\backslash ($ R $\backslash ).$

$($c$)(2$ points$)$ Write, but do not evaluate, an integral which gives the volume of the solid whose base is $\backslash ($ R $\backslash )$ and whose cross$-$sections perpendicular to the $\backslash ($ x $\backslash )-$axis are semicircles.