6. (15%) Find the Fourier series of the following periodic function f(x) with period $2\pi$. $$f(x) = \begin{cases} -1, & -\pi < x < 0 \\ 1, & 0 < x < \pi \end{cases}$$
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6. (15%) Find the Fourier series of the following periodic function f(x) with period $2\pi$. $$f(x) = \begin{cases} -1, & -\pi < x < 0 \\ 1, & 0 < x < \pi \end{cases}$$