Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.

Question

y = 8x − x^2, y = 12; about x = 2

Answer 1

each shell has volume

2πrh dx where
r = x-2
h = y

so,

v = ∫[2,6]2π(x-2)(8x-x^2) dx