If we have the surface $S$ delimited $Y$ and the following functions, what is the volume found by the revolution of the surface $S$ around the $Y$ axis.
$f(x)= (x- 5)^2$
$g(x)= x^2+ x+ 3$
We have found that $(0, 25) (2, 9)$ lie on the graph of $f$ and $(0, 3) (2, 9)$ lie on the graph of $g.$
I found my answer to be $\frac{88\pi}{3},$ but it seems oddly small. Here is my "starting point" formula :
$\int_0^2 2\pi(-11x+ 22)x{\rm d}x$
$-11x+ 22$ is the result of $f(x)- g(x)$
Can you tell me if I have the right result ? Did I do something wrong ?