Question: what is the difference between fourier integral and fourier transform?
Answer: Fourier integral of a function f is any Fourier integral, that satisfies x(t)=∫∞−∞y(ω)eiωtdω . ... The Fourier transform is usually defined with an expression such that it has to exist everywhere. Also the Fourier integral have to exist everywhere if we want the Fourier inversion theorem to be true.