Why when we apply Fourier series for $|\sin x|$ from $0 < x < \pi$ , we set $2L = 2\pi$?
Shouldn't it be $2L = \pi$?
In Schaum's Outline of Advanced Calculus book, there's a question that says:
"Expand $f(x) = \sin x, 0 < x < \pi$, in a Fourier cosine series.
A Fourier series consisting of cosine terms alone is obtained only for an even function. Hence, we extend the definition of $f(x)$ so that it becomes even. With this extension, $f(x)$ is then defined in an interval of length $2\pi$. Taking the period as $2 \pi$, we have $2L = 2\pi$ so that $L = \pi$."