What is the Integral of a Trigonometric Function with a Weird Substitution?

[LineIntegral]

Homework Statement

I need to calculate the integral:
$$\int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\mathrm{d}x$$

Homework Equations

The Attempt at a Solution

There is a tip: "try substituting $$y=\frac{\pi}{2}-x$$. I tried it and didn't get anywhere. I also tried several trigonometric identities.

Thanks in advance!

 

[snipez90]

Yeah you should probably try the suggested substitution again. Are you using the fact that sin(pi/2 - x) = cos x and cos(pi/2 - x) = sin x?

 

[LineIntegral]

Ok, I got it now... Thanks! :)