Suppose I have two function $f(x)$ and $g(x)$ such that for $x \in (\alpha, \beta )$ we have $f(x) \ge g(x) $.
I found an "exercise solution" that state that the volume given by the rotation of the area between $f$ and $g$ is:
$$\pi\int_\alpha^\beta (f(x) - g(x))^2 dx$$
but i think it's wrong and that it should be:
$$\pi\int_\alpha^\beta f(x)^2 - g(x)^2 dx$$
Who is right?