Difficult trignonometric Integral

[Mr.Brown]

Homework Statement

I need to find $$\int_{0}^{\pi}(sin(x)^{2n})dx$$.

My idea was to write sine in the exponential definition and use binomial theorem but i don´t really get anywhere :(

Any suggestions ?

 

[Office_Shredder]

If you integrate by parts, you get a recursive formula for $$\int (sin(x)^{2n})dx$$ in terms of something like $$sin(x)^{2n-1}$$ by differentiating sin to the power of 2n-1, and integrating a sin. My guess is that'll do the trick

 

[Mr.Brown]

hmm yea found that but i need an absolute formula if there even is one ?