Trivial question on Fourier Series

[Firepanda]

That is what I know, what I'm after is what do I do if my limits are different?

i.e I'm trying to do this in the interval of $$pi/4<x<3pi/4$$

obviously this isn't a case of -L<x<L

So I can't have a coefficient of 1/L outside the integral, what is my coefficient?

 

[Firepanda]

I imagine I could integrate from 0<x<3pi/4 with my coefficient being 8/3pi, then minusing the integral from 0<x<pi/4, with a coefficient of 8/pi.

 

[Firepanda]

Doesn't seem right though, my soln was closer when I knew I was doing it wrong

According to the solution I'm trying to get, it looks like I should be integrating the whole thing with a coefficient of 2/pi, can anyone confirm why this is please?

EDIT: nevermind, i think I have it

the original form took: L - -L = 2L, and did 2/2L = 1/L for the coeffiecient. So I did this. 3pi/4 - -pi/4 = pi (i.e pi=2L), so 2/pi.