Problem-solving approach for calculus homework

[lycraa]

figured it out myself, thanks

 

[HallsofIvy]

Normally, "the" function is the unit step function- u(x)= the largest integer less than or equal to x. As for finding its Fourier series, it is not periodic. I assume you are restricting it to $-\pi$ to $\pi$. Now, just use the standard integral formulas for the Fourier coefficients. Because the step function is constant over each integer interval, you will just be integrating sine and cosine over 8 intervals.