We presume the area being revolved around x=-2 is that shaded in the diagram below. Using the cylindrical shell method, the height of the shell is y, and the radius is 2+x. This makes our integral
.. [tex] V= \int\limits^1_0 {2\pi (x+2)x^{2}} \, dx = 2\pi (\frac{1}{4}1^{4}+ \frac{2}{3}1^{3})= \frac{11 \pi}{6}[/tex]
.. V ≈ 5.75959 . . . . cubic units
