Question

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

Answer 1

`pi` cubic units.

Explanation:

The volume of this torus-like solid is

`pi int((1+x)^2-(1-x)^2) dx`, from x = 9 to x =1

`=pi int 2x dx`, for the limits

`=pi[x^2]`, between x = 0 and x = 1

`pi` cubic units.