Quiz 2 — MA 16200 — June 21, 2022
Cian Nolan
For all questions, please show all relevant work.
1. (5 points) Let $R$ be the region bounded by the curves $y = \frac{1}{e^x}$, $y = 0$, $x = 0$ and $x = \ln 3$.
Find the volume of the solid generated when $R$ is revolved
about the $x$-axis.
2. (5 points) Let $R$ be the region bounded by the curves
$y = 2x$, $y = 3x + 1$, $x = 2$ and $x = 6$.
Using the shell method, find the volume of the solid generated when $R$ is revolved about the $y$-axis.