Weird Trigonometric Integral

1. Sep 20, 2009

LineIntegral

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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.

2. Sep 20, 2009

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?

3. Sep 20, 2009

LineIntegral

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