Calculus: Vol of Solid, rotating the region?

Question

Find the volume of the solid that is generated by rotating the region formed by the graphs of y=2x^2 and y=4x about the line x=3.

Answer 1

You can use multivariate calculus techniques for this, but you probably aren't studying that.

First find the bounds of integration from 4x=2x^2, so 0
Make shells of radius R which have area 2 Pi R h, then integrate them.

Here R = 3 - x, wherever you are in the solid, plus 3 to get to the axis of revolution. And h = upper function - lower function, so
h = 4x - 2x^2

now plug in and integrate:

V = 2 Pi Integral[(3-x)*(4x-2x^2)] from 0 to 2.
V = 2 Pi 16 / 3 = 32 Pi / 3

Answer 2

are you just going to post all your homework problems here?

i dont think you really like science and math