Question

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: $y = -2$.

          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: $y = -2$.

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.

Added by William M.

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