Problem $1.$ Let S be the region enclosed by the curves $\backslash ($ y$=$e$^\{\backslash$wedge$\}$ x$,$ y$=$e$^\{\backslash$wedge$\}\backslash \{-$x$\backslash \}\backslash )$ and $\backslash ($ x$=-2\backslash ).$

Let $\backslash ($ V $\backslash )$ be the volume of the solid obtained by rotating the region S about the x $-$axis.

$($a$)$ Express V using the cylindrical shells method.

$($b$)$ Express V using the washer method.

Do not evaluate V$.$

Problem $2.$ Let D be the region enclosed by the curves $\backslash (\backslash$mathrm$\{$y$\}=\backslash$ln $(\backslash$mathrm$\{$x$\}),\backslash$mathrm$\{$y$\}=-\backslash$mathrm$\{$x$\}+\backslash$mathrm$\{$e$\}+1\backslash )$ and $\backslash (\backslash$mathrm$\{$y$\}=0\backslash ).$

Let W be the volume of the solid obtained by rotating the region D about the y $-$axis.

$($a$)$ Express W using the cylindrical shells method.

$($b$)$ Express W using the washer method.

Do not evaluate V$.$