Dear all, first i'd like to apologize if my post is out of topic or in the wrong form but is my first experience with both Mathematica and this forum. I have a problem extracting the first Fourier coefficient of a function, which you can see in the image ![][2]

G(w) is a lorentzian function, lambda is a wavelenght, z is the space dependance, w the frequency and t the time

My problem is that if i define the function (the same separeting the terms) and then try to extract the first coefficient ( by definitio, using NIntegrate and the defining integral of the fourier coefficient), i get something different than if i just put the whole definition of the function in the integral. I hope my problem is clear, i don't know which result i should trust because it gives two different output just substituting to a function its expression, which is of course nonsense. Do you know what i can do?? Thank you very much.