find the area of the region inside one loop of the lemniscate r^2=4sin2theta
We really have very little do . . .Find the area of the region inside one loop of the lemniscate:
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.
There! . . .