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Question Number 140381 by Willson last updated on 07/May/21

$$\mathrm{f}\left(\mathrm{x}\right)={\mathrm{xe}}^{1-\mathrm{x}}$$$$\mathrm{Prove}\mathrm{that}\underset{\mathrm{n}\to +\mathrm{\infty }}{\lim }\sqrt{\mathrm{n}}{\underset{0}{\int }}^1{\left[\mathrm{f}\left(\mathrm{x}\right)\right]}^{\mathrm{n}}\mathrm{dt}=\sqrt{\frac{\pi }{2}}$$

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