3.
Here are four methods for finding the volume of a solid of revolution:
(1) Disk/washer method; integration respect to $x$.
(2) Disk/washer method; integration respect to $y$.
(3) Shell method; integration with respect to $x$.
(4) Shell method; integration respect to $y$.
In each part, the region $R$ is revolved around the given axis to form a solid $S$. Which method
is the best for computing the volume of $S$? No justification required. (You don't need to
write down any integrals or do any algebra; just state which of the four methods is best.)
(a) $R$ is bounded by $x = \ln y$, $y = 0$, $x = 0$, and $x = 1$. Axis of revolution: $x = -2$.
(b) $R$ is bounded by $x = \ln y$, $y = 0$, $x = 0$, and $x = 1$. Axis of revolution: $y = -2$.
(c) $R$ is bounded by $xy = 1$, $x = 0$ and $y = 1$ and $y = 2$. Axis of revolution: $y = -2$.
