The value of the integral $\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{ an x}} \mathrm{~d} x$ is

Question

The value of the integral $\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{	an x}} \mathrm{~d} x$ is

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Since } \int_0^{\frac{\pi}{2}} \frac{\cot ^{\mathrm{n}} x}{	an ^{\mathrm{n}} x+\cot ^{\mathrm{n}} x} \mathrm{~d} x=\frac{\pi}{4} \ & \int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{	an x}} \mathrm{~d} x=\frac{\pi}{4}\end{aligned}$

The value of the integral $\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}}…

Solution