The problem is related to polar curves. most of the topics i need to do are easy (finding the slope, finding the area etc.) What i'm facing problems with is that when I find the area, I don't know how to find the limits. 1. The problem statement, all variables and given/known data Sample problem: Find the area of the region in the plane enclosed by the cardioid r=4+(4sinθ) 2. Relevant equations b A = ∫ (1/2)(r^2) dθ a 3. The attempt at a solution Graphing the curve is no biggie, I use my calculator. The problem is when I use the equation to find the Area, I don't know what the interval is I don't know 'b' and 'a' are. I have a calculus book, an AP calculus book, and a pre-calculus book. None of the books tell you how to find the interval. In their solved questions, they tell you that in the solution. The problem I wrote above is an example also. They tell you the interval is (for the q above) 0 to 2π(pi) but how do i know that what about other questions. Another example: Find the area inside the smaller loop of the limacon r=1+(2cosθ) Here they say the limits are (2π(pi))/(3) to (4π(pi))/3 The exact explanation to this in the book is: (for first question) "Because r swoops out the region as θ goes from 0 to 2π(pi), these are our limits of integration. (For 2nd q) Because in the inner loop, r sweeps out the region as θ goes from (2π(pi))/(3) to (4π(pi))/3, these are our limits of integration. But why!? What does r swoops mean. How do I know the limits!? please help!