Did you sketch the curve? . . . It always helps.Find the area of the region enclosed by: .
i'm guessing the equation would be set up as: . . . . . um, not quite
but what would my limits be?
It is a figure-8, centered at the origin, tipped 45° clockwise.
. . Note: There are two loops to consider.
The limits occur when ,
. . when the curve leaves and returns to the origin.
We have: .
. . Then: .
So one loop is formed for: .
The formula for polar area is: .
The area of one loop is: .
For the total area of the lemiscate, multiply that result by 2.