Question

1. Obtain the Fourier series of f (x) x- x2 in the range -π

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

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 a0 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].

Step-by-step explanation:

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