Figure N7–20(Note that we obtained the same result using washers in Example 8.)
NOTE: In Examples 32 and 33 we consider finding the volumes of solids
using shells that lead to improper integrals.
‡Examples 10–12 involve finding volumes by the method of shells. Although shells are not included in the
Topic Outline, we include this method here because it is often the most efficient (and elegant) way to find a
volume. No question requiring shells will appear on the AP exam.
BC ONLYC. ARC LENGTH
If the derivative of a function y = f (x) is continuous on the interval a x b,
then the length s of the arc of the curve of y = f (x) from the point where x = a to
the point where x = b is given by