$1.(20$ points$)$ Let $\backslash ($ R $\backslash )$ be the region in the first quadrant of the plane, bounded by the curve $\backslash ($ x$=-$y$^\{2\}+2$ y$+3\backslash )$ and coordinates axes. Let $\backslash ($ V $\backslash )$ be the solid obtained by rotating $\backslash ($ R $\backslash )$ about the $\backslash ($ x $\backslash )-$axis.

a$/(10$ points$)$ Find the formulas to compute the volume of $\backslash ($ V $\backslash )$ using the disc method and the shell method.

$\backslash (\backslash$mathrm$\{$b$\}/(10\backslash )$ points$)$ Compute the volume of $\backslash ($ V $\backslash )$ using one of the formulas obtained in part a$/.$