Question

Assume f and g are continuous with ​f(x)greater than or equals ​g(x)greater than or equals0 on​ [a,b]. The region bounded by the graphs of f and g and the lines xequals a and xequals b is revolved about the y axis. Write the integral given by the shell method that equals the volume of the resulting solid.

Answer 1

We have $f(x)$ and $g(x)$ where

$f(x)\geq g(x)\geq 0$ on the closed interval $[a,b]$.

The area enclosed by functions can be 0 if $f(x)=g(x)=n$ where n is constant and $n\geq0$. Let S denote the surface we must find difference of f and g to find the area encapsulated by f and g.

$S=\int_{a}^{b}f(x)-g(x)dx=\int_{a}^{b}f(x)dx-\int_{a}^{b}g(x)dx$

Hope this helps.