Extend you function (represented by dotted line) in the way shown below.
Since we can extend periodically by where .
The Fourier series would be given as, .
Since on is an even function it forces .
Thus, for .
fin the cosine series fo r the function defined by
f(x) = 1/4 - x, 0<= x < 1/2
f(x) = x - 3/4, 1/2<=x<=1
for this, I chose L = 1/2, so t = 2pie x
so the integral limits are 0 to pie and pie to 2 pie...
How do I get it to go to -pie to pie? help!
It seems you can do your problem two ways. One way is the approach I was trying to do above with but you can also do it with . Because if you take the function on and extend it periodically you would get the same function. Thus, in that case you can pick too.i see that f(-1/2) = f (1/2)
so L = 1/2
so f(x) = f(x-1/2)