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854

Part of 2012 Today's Calculation Of Integral

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Today's calculation of Integral 854

Source:

11/17/2012
Given a figure F:x2+y23=1F: x^2+\frac{y^2}{3}=1 on the coordinate plane. Denote by SnS_n the area of the common part of the n+1′sn+1' s figures formed by rotating FF of k2nπ (k=0, 1, 2, ⋯ , n)\frac{k}{2n}\pi\ (k=0,\ 1,\ 2,\ \cdots,\ n) radians counterclockwise about the origin. Find lim⁡n→∞Sn\lim_{n\to\infty} S_n.
calculusintegrationanalytic geometrygeometrylimitconicsellipse