From Rogawski 2e section 6.4, exercise 31.
Sketch the region between the x-axis and the graph of $f(x) = 33 - x^2$ for
$0 \le x \le 2$. Part (3) of this problem asks you to compute volume of the solid
generated by rotating this region about the x-axis. You can compute that last
answer with your favorite method, but the first two parts of this problem require
you to use the Cylindrical Shell method.
(1) Horizontal strips for the lower part of the region have constant width; the
solid obtained by rotating that whole lower part has volume computed by
$\int_a^b \Box dy$
help (formulas)
where the limits of integration are $a = \Box$ and $b = \Box$ help (numbers)
(2) Horizontal strips for the upper part of the region have widths which vary with
y; the solid obtained by rotating that whole upper part has volume computed by
$\int_c^d \Box dy$
help (formulas)
where these limits of integration are $c = \Box$ and $d = 0$ help (numbers)
(3) The whole solid has volume $\Box$ cubic units. help (numbers)
