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Question Number 33333 by prof Abdo imad last updated on 14/Apr/18

let hive  I_n = ∫_0 ^(π/2)  (sinx)^n  dx  prove that  I_n  ∼  (√(π/(2n))) (n→∞)

$${let}\:{hive}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\left({sinx}\right)^{{n}} \:{dx} \\ $$$${prove}\:{that}\:\:{I}_{{n}} \:\sim\:\:\sqrt{\frac{\pi}{\mathrm{2}{n}}}\:\left({n}\rightarrow\infty\right) \\ $$$$ \\ $$

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