Revolve the region bounded by y = 4x and y = x^2 about the y-axis. In cubic units, the resulting volume is

Answer 1

First you have to find where they intersect, that is easy
....
I am sure you can see that is (0,0) and (4,16)
The radius of the outer ring is √y, the radius of the inner ring is y/4
Vol = π∫(y - y^2/16) dy
= π[ y^2/2 - y^3/48] from 0 to 16
= π[128 - 256/3 - 0) = (128/3)π

you better check my arithmetic, getting sloppy in my old age.