1. The problem statement, all variables and given/known data Find the area of the region that consists of all points that lie within the circle r = 1 but outside the polar equation r = cos(2θ) 2. Relevant equations A = ∫ 1/2 (r2^2 - r1^2) dθ, where r2 is outer curve and r1 is inner curve. 3. The attempt at a solution Here is what the graph looks like if you want to see it: http://www.wolframalpha.com/input/?i=r+=+cos(2x)+polar Ok so first I had to find out the limits for my integral. I set: 1 = cos(2θ) and got that θ = ∏. Now I made my integral, but instead of going from -∏ to ∏ I went from 0 to ∏ and multiplied it by 2 A = 2 ∫ 1/2 [(1^2) - (cos(2θ)^2)] dθ, from 0 to ∏ A = ∫ [ (1) - (1/2 cos(4θ) +1)] dθ, from 0 to ∏ I solved it and received: ∏ - ∏/2 Which equals ∏/2. Just want to know if I did it right. The main part I was worried about was the limits for my integral.