Areas of regions Make a sketch of the region and its bounding curves. Find the area of the region.
The region inside the rose r = 4 sin 2θ and inside the circle r = 2
We find the area between the the rose r = 4 sin 2θ and inside the circle r = 2
The two curves intersect where
Then the area becomes
Then we just need to double our answer to find the entire area bound by the lemniscate.
so the area we seek is