Question $1(10$ points$)$ Let $\backslash ($ R $\backslash )$ be the region bounded by the parabola $\backslash ($ y$=\backslash )\backslash (2$ x$^\{2\}+2\backslash )$ and the line $\backslash ($ y$=10\backslash ).$

$($a$)(2$ points$)$ Sketch the region $\backslash ($ R $\backslash ),$ and find its area.

$($b$)(3$ points for solution, $1$ point for clarity and organization of the solution$)$ Set up the integral to calculate the volume of the solid obtained by rotating the region $\backslash ($ R $\backslash )$ around the $\backslash ($ x $\backslash )-$axis. $($c$)(3$ points for solution, $1$ point for clarity and organization of the solution$)$ Set up the integral calculating the volume of the solid obtained by rotating the region $\backslash ($ R $\backslash )$ around the line $\backslash ($ y$=10\backslash ).$