MathDB
Today's calculation of Integral 854

Source:

November 17, 2012
calculusintegrationanalytic geometrygeometrylimitconicsellipse

Problem Statement

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.
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