Answer
$\dfrac{162 \pi}{5}$
Work Step by Step
The volume of a solid by using the washer method can be calculated as:
$V=\pi \int_{m}^{n} (R^2_{outer}-r^2_{inner}) \ dx \\=\pi \int_{-1}^{2} [(x+4)^2-(x^2+2)^2] \ dx \\=\pi \int_{-1}^{2} (8x-x^4-3x^2+12) \ dx \\=\pi [4x^2 -\dfrac{1}{5} x^5 -x^3 +12 x ]_{-1}^2 \\=\pi [\dfrac{128}{5}+\dfrac{34}{5}] \\=\dfrac{162 \pi}{5}$
