Question

How do you find the volume of `y=x^2` going from [0, 2] on the x-axis and [0, 4] on the y-axis?

Answer 1

`6pi` cubic units

Explanation:

Volume = `pi int x^2dy`, with y from 2 to 4 and x from `y= x^2`.

`=pi int ydy,` with y from 2 to 4

`=pi[y^2/2],` between the limits 2 and 4

`=pi/2(4^2-2^2)=6pi` cubic units.