Linear Algebra: Fourier Series and Square Wave

[jrunyon2]

I have been working on this problem for a couple days now and have been frustrated with it from the start...

I need to find the Fourier Series representation of the given function for the square wave:

f(t) = 1 on the interval -pi/2 to pi/2
= 0 everywhere else


I seem to be having problems with the interval over which to integrate. Should I be integrating from -pi/2 to pi/2 with a scaled cosine and sine function to find the coefficients of the Fourier Series? The problem has been hanging me up because there is only a single square wave, not a full set alternating from -1 to 1. Any thoughts?

 

[Unco]

The square wave must repeat; the function has period 2pi. One fundamental part is from -pi/2 to 3pi/2. The integral limits are then -pi/2 to pi/2 (for f(t)=1) and pi/2 to 3pi/2 (for f(t)=0), the latter being zero. Also note the a_n terms will be zero.