## watchmath 5 years ago 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 :).

1. watchmath

I forgot the dx at the end :)

2. anonymous

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

3. anonymous

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

4. anonymous

Should I proceed or let others try?!

5. watchmath

That is already a solution I guess :D

6. anonymous

I guess.

7. anonymous

:D

8. anonymous

i havea guess. let me see if can prove it

9. anonymous

@Michael: Thanks! :D