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calculate-lim-n-0-n-1-t-n-n-arctan-nt-dt-




Question Number 98945 by mathmax by abdo last updated on 17/Jun/20
calculate lim_(n→+∞)   ∫_0 ^n (1−(t/n))^n arctan(nt)dt
$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\:\int_{\mathrm{0}} ^{\mathrm{n}} \left(\mathrm{1}−\frac{\mathrm{t}}{\mathrm{n}}\right)^{\mathrm{n}} \mathrm{arctan}\left(\mathrm{nt}\right)\mathrm{dt} \\ $$

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