# 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?

Jan 24, 2017

$6 \pi$ cubic units

#### Explanation:

Volume = $\pi \int {x}^{2} \mathrm{dy}$, with y from 2 to 4 and x from $y = {x}^{2}$.

$= \pi \int y \mathrm{dy} ,$ with y from 2 to 4

$= \pi \left[{y}^{2} / 2\right] ,$ between the limits 2 and 4

$= \frac{\pi}{2} \left({4}^{2} - {2}^{2}\right) = 6 \pi$ cubic units.