Hello, leinadwerdna!

We really have very little do . . .Find the area of the region inside one loop of the lemniscate:

Formula: .

If you recognize the curve or can make a sketch, you see that

. . it is a figure-8 tipped so the loops are in Quadrants 1 and 3.

We already have . . . all we need are the limits.

Set

There!. . .

Got it?