So I am learning how to do Fourier series expansions by writing the function expression from given graphs:
To find the series, we calculate A0,An and Bn and plug those values in the main Fourier series formula and get a few trigonometric components expansions. However, the problem I am facing is both my An and Bn come to 0 after doing the integration which is unusual. I have written the function below with the limits I am using in the math and also attached a photo of the figure. $$ f(x)= \begin{cases} 0&, -2<x<1 \\ 5&, -1<x<1 \\ 0&, 1<x<2 \\ \end{cases} $$ I would really appreciate it if anyone solve this math/tell me what am I doing wrong. Thank you.