# Volume using Cylindrical Shells

1. Oct 10, 2011

### silverbell

1. The problem statement, all variables and given/known data

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y = 4+3x-x^2 and y+x=4 about the y-axis. Below is a graph of the bounded region.

2. Relevant equations

V = ∫ a to b 2 pi x f(x)
3. The attempt at a solution

∫from 0 to 4 2 pi (4-x)(4)

∫from 0 to 4 2 pi (16-4x)

∫ [16-4(4) - (16- 4(0))]

0 - 12

-12

2. Oct 10, 2011

### Staff: Mentor

$$2\pi \int_0^4 x(4x - x^2)dx$$