Hello, Ahplym!
tonio told you what has to be done.
But it takes some Olympic-level gymnastics.
We have: .
Differentiate: .
Square: .
Take the square root: .
We have: .
The graph is an astroid (a hypocycloid of four cusps).
It is symmetric to both axes and the Origin.
We can integrate from 0 to and multiply by 4.
. .
. . . .