Answer
$\dfrac{ 376 \pi }{15}$
Work Step by Step
The disk method to compute the volume of revolution: When the function $f(x)$ is continuous and $f(x) \geq 0$ on the interval $[m,n]$, then the volume of a solid obtained by rotating the region under $y=f(x)$ over an interval $[m,n]$ about the x-axis is given by:
$V= \pi \int_{m}^{n} [f(x)]^2) \ dx$
Now, $V=\pi \int_{0}^{2} [(x^2+2)^2] \\ =\pi \int_0^2 [x^4+4x^2+4] \ dx \\=\pi [\dfrac{x^5}{5}+\dfrac{4x^3}{3}+4x]_0^2\\=\pi [\dfrac{(2^5)}{5}+\dfrac{4(2^3)}{3}+4(2)] \\=\dfrac{ 376 \pi }{15}$
