Question

How do you find the volume of `y=2x^2`; `y=0`; `x=2` revolved about the x axis?

Answer 1

There is a mistake: `x=0` (not y) and `x=2`
See explanation below

Explanation:

The x-axis is the revolution axis, then

`V=int_0^2piy^2dx=4piint_0^2x^4dx=4pi/5x^5]_0^2=128pi/5`