Why can non-periodic functions be expressed as a Fourier integral?

[nnvkct]

http://img96.imageshack.us/img96/4240/hinhcc9.jpg

I'm studying on Fourier Transform. And the only thing I don't understand about it still now is the problem about Fourier Integral with non-periodic function. Why we can write it in the form above ? Please help me. I appreaciate any help.

Best regard.

 

[Fredrik]

You don't have to figure that out by yourself. That stuff is a theorem that isn't easy to prove, but if you're interested you can find the proof in any textbook on Fourier analysis.

 

[HallsofIvy]

First, what definition of Fourier Integral are you using? Once you have answered that we may be able to help you see how to change it to the form you want.