Question

Determine the volume of the solid of revolution which is formed when the enclosed are between y=f(x) and y=g(x) is rotated about the y axis.

Answer 1

By the shell method

$$V=\displaystyle\int_{a}^b(2\pi x)\big[f(x)-g(x)\big]dx,$$

$f(x)\geq g(x)$ on $[a, b]$