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Omni-MATH / Suppose that f is a function from R to R such that f(x)+f(1−(1)/(x))=arctanx for all real x≠0. (As usual, y=arctanx means −π/2<y<π/2 and tany=x.) Find ∫₀¹f(x) dx.

Problem

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problem

Suppose that ff is a function from R\mathbb{R} to R\mathbb{R} such that f(x)+f(1−1x)=arctanx f(x) + f\left( 1 - \frac{1}{x} \right) = \arctan x for all real x≠0x \neq 0. (As usual, y=arctanxy = \arctan x means −π/2<y<π/2-\pi/2 < y < \pi/2 and tany=x\tan y = x.) Find ∫01f(x)dx. \int_0^1 f(x)\,dx.
Plain-text mathematical notation (without MathML)
Suppose that f is a function from R to R such that f(x)+f(1−(1)/(x))=arctanx for all real x≠0. (As usual, y=arctanx means −π/2<y<π/2 and tany=x.) Find ∫₀¹f(x) dx.
Original LaTeX notation
Suppose that $f$ is a function from $\mathbb{R}$ to $\mathbb{R}$ such that \[ f(x) + f\left( 1 - \frac{1}{x} \right) = \arctan x \] for all real $x \neq 0$. (As usual, $y = \arctan x$ means $-\pi/2 < y < \pi/2$ and $\tan y = x$.) Find \[ \int_0^1 f(x)\,dx. \]

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Source and history

task_id
0e24cb9c-2a62-5eac-a680-37dcdcfde28e
task_key
test--0e24cb9c-2a62-5eac-a680-37dcdcfde28e
task_revision_id
1
config / split
/ test

Official source

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