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 :).

Answer 1

I forgot the dx at the end :)

Answer 2

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

Answer 3

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

Answer 4

Should I proceed or let others try?!

Answer 5

That is already a solution I guess :D

Answer 6

I guess.

Answer 7

:D

Answer 8

i havea guess. let me see if can prove it

Answer 9

@Michael: Thanks! :D