$2.$ Let $\backslash ($ R $\backslash )$ be the region bounded by $\backslash ($ y$=10,$ x$=2\backslash ),$ and $\backslash ($ y$=$e$^\{$x$\}\backslash ).$ Let $\backslash ($ S $\backslash )$ be the solid obtained by revolving $\backslash ($ R $\backslash )$ around the $\backslash ($ y $\backslash )-$axis.

a$.[4$ pts$]$ Sketch $\backslash ($ R $\backslash )$ and $\backslash ($ S $\backslash ).$ Clearly label any bounds and intersection points in $\backslash ($ R $\backslash ).$

b$.[8$ pts$]$ Find the volume of $\backslash ($ S $\backslash ).($I think the shell method is easier for this. But the washer method works too. Either option will require an integration by parts for the integral.$)$