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evaluate-the-inequality-for-n-2-pi-2-1-n-1-n-1-n-lt-1-n-pi-2-sin-t-1-n-dt-




Question Number 94093 by MAB last updated on 16/May/20
evaluate the inequality for n≥2  ((π/2)−(1/n))(1/( (n)^(1/n) ))<∫_(1/n) ^(π/2) ((sin(t)))^(1/n) dt
$${evaluate}\:{the}\:{inequality}\:{for}\:{n}\geqslant\mathrm{2} \\ $$$$\left(\frac{\pi}{\mathrm{2}}−\frac{\mathrm{1}}{{n}}\right)\frac{\mathrm{1}}{\:\sqrt[{{n}}]{{n}}}<\int_{\frac{\mathrm{1}}{{n}}} ^{\frac{\pi}{\mathrm{2}}} \sqrt[{{n}}]{{sin}\left({t}\right)}{dt} \\ $$

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