Answer
$\frac{832\pi}{15}$
Work Step by Step
Setup the integration using washer method about the line x=5.
$ 2\pi \int_0^2 [(5-y^2)^2 - (1)^1]dy$, It is easier to use the interval [0,2] because the graph is symmetric and then just multiply the integration by two.
$2\pi \int_0^2 (25-10y^2 +y^4 -1)dy$
$2\pi \int_0^2 (y^4 -10y^2 +24)dy$
$2\pi [\frac{1}{5}y^5 - \frac{10}{3}y^3 +24y]_0^2$
$2\pi(\frac{32}{5}- \frac{80}{3}+48)-0$
$\frac{832\pi}{15}$
