I am getting confused on how to determine the bounds for integration for this problem. My reasoning is as follows:
$ f(x) = x $ for $ 0 < x < 1 $ and $f(-x) = -x = -f(x)$ therefore $f(x)$ is odd and the cosine term of the series will cancel out. Will the $ a_0 $ term cancel out as well? I was expecting it would since my integration is from $-1/2$ to $1/2$.
I say that because, $ f(x+P) = f(x) $ taking P: period and $ P = 2L $ therefore if my interval is [0,1] then: $$ P = 2L = 1 $$ and $$ L = 1/2 $$
That way the bounds of my integral are $[-1/2,1/2]$. But in the solutions it is indicated that the bounds of integration are $[0,1]$, which I think is the right answer cause we always find the Fourier series over the entire period and in this case it would be [0,1]. What am I understanding incorrectly? You can find the problem here: http://exampleproblems.com/wiki/index.php/FS8 Thanks!