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lim-n-1-3pi-pi-2pi-x-arctan-nx-dx-n-




Question Number 160439 by qaz last updated on 29/Nov/21
lim_(n→∞) ((1/(3π))∫_π ^(2π) (x/(arctan (nx)))dx)^n =?
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{3}\pi}\int_{\pi} ^{\mathrm{2}\pi} \frac{\mathrm{x}}{\mathrm{arctan}\:\left(\mathrm{nx}\right)}\mathrm{dx}\right)^{\mathrm{n}} =? \\ $$

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