Question

Let r be the regeion bounded by y=x^2, x=1, and y=0. find the volume of the solid generated when r is revolved around x=-2

Answer 1

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
..
`V= \int\limits^1_0 {2\pi (x+2)x^(2)} \, dx = 2\pi ((1)/(4)1^(4)+ (2)/(3)1^(3))= (11 \pi)/(6)`
.. V ≈ 5.75959 . . . . cubic units