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Differential EquationsSuperchallengeBoundary Values & Fourier Series

Boundary Values & Fourier Series · Superchallenge problem

Among all functions asin⁡x+bsin⁡2xa\sin x + b\sin 2x, find the minimum possible value of ∫−ππ(x−asin⁡x−bsin⁡2x)2dx\displaystyle\int_{-\pi}^{\pi}\left(x - a\sin x - b\sin 2x\right)^2dx.