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# Fourier Series HELP watch

1. f(x)=x, for 0≤x≤π

The function is then defined on the interval −π≤x≤π by extending it as an even function. It is then defined on the whole real line by extending it as an 2π-periodic function.

Calculate the Fourier series of f(x).

How do I do this? I'm unsure how to tackle this as I don't know what interval I'm supposed to calculate the Fourier series for.
2. (Original post by victoriarty)
f(x)=x, for 0≤x≤π

The function is then defined on the interval −π≤x≤π by extending it as an even function. It is then defined on the whole real line by extending it as an 2π-periodic function.

Calculate the Fourier series of f(x).

How do I do this? I'm unsure how to tackle this as I don't know what interval I'm supposed to calculate the Fourier series for.
I don't think it matters whether you choose −π≤x≤π or 0≤x≤2π. The coefficients should come out the same.
3. (Original post by victoriarty)
f(x)=x, for 0≤x≤π

The function is then defined on the interval −π≤x≤π by extending it as an even function. It is then defined on the whole real line by extending it as an 2π-periodic function.

Calculate the Fourier series of f(x).

How do I do this? I'm unsure how to tackle this as I don't know what interval I'm supposed to calculate the Fourier series for.
Preferably you choose your integration region to be symmetric over .

Here, this is an even function so it will have a first term . Note that is an even function, therefore which simplifies the integral down.

Similarly, we have

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