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0-pi-2-sin-1-n-d-




Question Number 121914 by Dwaipayan Shikari last updated on 12/Nov/20
∫_0 ^(π/2) (sinθ)^(−(1/n)) dθ
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({sin}\theta\right)^{−\frac{\mathrm{1}}{{n}}} {d}\theta \\ $$
Commented by Dwaipayan Shikari last updated on 12/Nov/20
(1/2).((Γ((1/2)−(1/(2n)))Γ((1/2)))/(Γ(1−(1/(2n)))))   (n>1)
$$\frac{\mathrm{1}}{\mathrm{2}}.\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}{n}}\right)\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)}{\Gamma\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{n}}\right)}\:\:\:\left({n}>\mathrm{1}\right) \\ $$

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