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Question Number 117216 by bobhans last updated on 10/Oct/20

$$\underset{0}{\stackrel{\pi /2}{\int }}\frac{\mathrm{dx}}{\sqrt{\sin \mathrm{x}}}=?$$$$$$

Answered by TANMAY PANACEA last updated on 10/Oct/20

$$2{\int }_0^{\frac{\pi }{2}}{sin}^{2p-1}{xcos}^{2q-1}xdx=\frac{\lceil \left(p\right)\lceil \left(q\right)}{\lceil p+q)}$$$$\frac{1}{2}\times 2{\int }_0^{\frac{\pi }{2}}{\left(sinx\right)}^{2\times \frac{1}{4}-1}{cos}^{2\times \frac{1}{2}-1}dx$$$$=\frac{1}{2}\times \frac{\lceil \left(\frac{1}{4}\right)\times \lceil \frac{1}{2}}{\lceil (\frac{1}{4}+\frac{1}{2})}$$

Commented by bobhans last updated on 10/Oct/20

$$\mathrm{this}\mathrm{is}\mathrm{\Gamma }=\mathrm{gamma}\mathrm{function}?$$

Commented by TANMAY PANACEA last updated on 10/Oct/20

$$yessir$$

Commented by bobhans last updated on 10/Oct/20

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

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