0-pi-2-dx-sin-x-

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

\underset{0}{\int^{π / 2}} \frac{dx}{\sqrt{\sin x}} = ?

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

2 \int_{0}^{\frac{π}{2}} {s i n}^{2 p - 1} {x c o s}^{2 q - 1} x d x = \frac{⌈ (p) ⌈ (q)}{⌈ p + q)}

\frac{1}{2} \times 2 \int_{0}^{\frac{π}{2}} {(s i n x)}^{2 \times \frac{1}{4} - 1} {c o s}^{2 \times \frac{1}{2} - 1} d x

= \frac{1}{2} \times \frac{⌈ (\frac{1}{4}) \times ⌈ \frac{1}{2}}{⌈ (\frac{1}{4} + \frac{1}{2})}

Commented by bobhans last updated on 10/Oct/20

this is Γ = gamma function ?

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

y e s s i r

Commented by bobhans last updated on 10/Oct/20

thank you sir

Facebook Tweet Pin