# How do you find the volume of the region enclosed by the curves y=x, y=-x, and x=1 rotated about y=-1?

##### 1 Answer
Dec 3, 2016

$\pi$ cubic units.

#### Explanation:

The volume of this torus-like solid is

$\pi \int \left({\left(1 + x\right)}^{2} - {\left(1 - x\right)}^{2}\right) \mathrm{dx}$, from x = 9 to x =1

$= \pi \int 2 x \mathrm{dx}$, for the limits

$= \pi \left[{x}^{2}\right]$, between x = 0 and x = 1

$\pi$ cubic units.