Chapter 17.6, Problem 75E

Surfaces of revolution –single variable Let f be the difference and positive on the interval [a, b]. Let S be the surface generated when the graph of f on [a, b] is revolved about the x−axis.

Use Theorem 17.14 to show that the area of S (as given in Section 6.6) is

     ${\displaystyle {\int }_a^{b}2\pi f(x)\sqrt{1+f\text{'}{(x)}^2}}dx.$