A fun classic problem
Compute
$$\int_0^{\pi/2}\frac{\sin^{2011}x}{\sin^{2011}x+\cos^{2011}x}$$
If you have seen this problem before, please let others try first :).

Question

A  fun classic problem
Compute
$$\int_0^{\pi/2}\frac{\sin^{2011}x}{\sin^{2011}x+\cos^{2011}x}$$
If you have seen this problem before, please let others try first :).

watchmath · Answer

I forgot the dx at the end :)

anonymous · Answer

Oh I think I have solved a similar problem to this.

anonymous · Answer

The approach I used to solve that problem was:
$$\int\limits_{0}^{a}{f(x) \over f(x)+f(a-x)}dx=\int\limits_{0}^{a}{f(a-x) \over f(x)+f(a-x)}dx$$

anonymous · Answer

Should I proceed or let others try?!

watchmath · Answer

That is already a solution I guess :D

anonymous · Answer

I guess.

anonymous · Answer

:D

anonymous · Answer

i havea guess.  let me see if can prove it

anonymous · Answer

@Michael: Thanks! :D