Putnam 2016 A3
Posted: Mon Dec 05, 2016 6:04 pm
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ such that
\begin{equation} f(x)+f\left(1-\frac1x\right)=\arctan x \quad \text{forall} \; x \neq 0\end{equation}
(As usual $y = \arctan x $ means $-\pi/2<y<\pi/2$ and $\tan x = y$.)
Evaluate the integral $\displaystyle \int_0^1 f(x) \, {\rm d}x$.
\begin{equation} f(x)+f\left(1-\frac1x\right)=\arctan x \quad \text{forall} \; x \neq 0\end{equation}
(As usual $y = \arctan x $ means $-\pi/2<y<\pi/2$ and $\tan x = y$.)
Evaluate the integral $\displaystyle \int_0^1 f(x) \, {\rm d}x$.