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Putnam 2016 A3

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December 4, 2016
PutnamPutnam 2016Putnam calculusmapping

Problem Statement

Suppose that ff is a function from R\mathbb{R} to R\mathbb{R} such that f(x)+f(1−1x)=arctan⁡xf(x)+f\left(1-\frac1x\right)=\arctan x for all real x≠0.x\ne 0. (As usual, y=arctan⁡xy=\arctan x means −π/2<y<π/2-\pi/2<y<\pi/2 and tan⁡y=x.\tan y=x.) Find ∫01f(x) dx.\int_0^1f(x)\,dx.
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