Hello, clev88!
Find the area of the region that is outside and inside is a circle with radius 2.
is a lemniscate ("figure 8").
The graph looks like this . . . Code:

...*...
*::::::::::*
*::::::::::::::*
*::::::::::::::::*
::::::::::::::::::
*::::::::::::::::::*
*::::::::::::::::::*
*:::::::o o o:::::::*
*:::o  o:::*
:o  o:
o  o
*  *
o *  * o
  o     *     o  
o *  * o
*  *
o  o
:o  o:
*:::o  o:::*
*:::::::o o o::::::::*
*::::::::::::::::::*
*::::::::::::::::::*
::::::::::::::::::
*::::::::::::::::*
*::::::::::::::*
*::::::::::*
*

Due to the symmetry, we can find the area in quandrant 1 and multiply by 4.
Intersection: .
. .
Then: .
Got it?