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Re: Area between two circles

Re: Area between two circles

Re: Area between two circles

Re: Area between two circles

Post #3 is correct. The integral expressions should be swapped (and 2 added) in post #2: WolframAlpha.

It is easy to find the area without calculus. Using notations from post #2, we need to find twice the area of the circular segment PLRQ. Then , so the angle is 60 degrees. Therefore, the central angle POR of the segment is 120 degrees. The area of the corresponding circular sector is , and the area of the triangle POR is . From here, the area of PLRQ is , and the final answer is twice that.