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For both parts consider the region $\backslash ($ R $\backslash )$ bounded by $\backslash ($ y$=\backslash$ln x$,$ y$=1\backslash ),$ and $\backslash ($ x$=1\backslash ).$

$($a$)(1$ point$)$ Sketch the region $\backslash ($ R $\backslash )$ in the $\backslash ($ x y $\backslash )-$plane. Be sure to shade$/$color the region and clearly indicate any intersection points.

$($b$)(3$ points$)$ Find the volume of the solid obtained by rotating the region $\backslash ($ R $\backslash )$ about the $\backslash ($ y $\backslash )-$axis.