Hello, tomobson!

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 areloops to consider.two

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 thetotalarea of the lemiscate, multiply that result by 2.