Hi there. I'm starting with the Fourier transforms, and I'm having some trouble with my first exercise on this topic.

The problem says: Given (H(x) is the Heaviside unit step function).

a) Consider the odd extension for f and find its Fourier integral representation.

b) Using the previous incise calculate the value for

Well, for a) I think I should get the fourier transfor for the sign function, I don't know if this is right, but anyway I've defined the function like this:

Then the Fourier integral representation:

But g(x) is odd, then:

And the thing is that the integral for the cosine diverges as I see it, but I'm probably doing something wrong.

Help please