1. The problem statement, all variables and given/known data Find the area inside the larger loop and outside the smaller loop of the limacon r=.5+cosθ Picture here http://www.wolframalpha.com/input/?i=r=.5+costheta 2. Relevant equations Area = .5∫r^2 3. The attempt at a solution To get the area of the outer loop, you just get the value of the entire area, and then just subtract the area of the inner loop. I use two integrals for this To start, i get the area of the inner loop. r=.5+cosθ -.5=cosθ θ=120 degrees or 2pi/3. and 240 degrees, or 1.33pi. .5∫(.5+cosθ)^2 evaluated at 2pi/3(lower bound on integral) and 1.33pi(upper bound on integral). I get .135879 Now, I have to get the area of the entire limacon. I use the bounds zero and 2pi .5∫(.5+cos)^2 which 2pi as upper limit and 0 as lower limit. I get 2.35619 Now, 2.35619-.135879 i get 2.2203. This is the wrong answer though, the correct answer is 2.08. If i was to subtract another .135879 from 2.2203, that would give me the right answer. But why do i have to subtract another .135879? I should be getting the correct answer with the set up i have.