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find-lim-n-0-n-1-x-n-2n-arctan-pix-n-dx-




Question Number 119837 by mathmax by abdo last updated on 27/Oct/20
find lim_(n→+∞)    ∫_0 ^(√n) (1−(x/( (√n))))^(√(2n))  arctan(((πx)/n))dx
$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\:\:\int_{\mathrm{0}} ^{\sqrt{\mathrm{n}}} \left(\mathrm{1}−\frac{\mathrm{x}}{\:\sqrt{\mathrm{n}}}\right)^{\sqrt{\mathrm{2n}}} \:\mathrm{arctan}\left(\frac{\pi\mathrm{x}}{\mathrm{n}}\right)\mathrm{dx} \\ $$

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