## Integral homework problems

Hi everyone,

Can anyone show me how the property
$$\frac{1}{2\pi} \int ^{\infty} _{-\infty} e^{i\omega x}d\omega= \delta(x)$$
holds.

Thanks,
 PhysOrg.com science news on PhysOrg.com >> King Richard III found in 'untidy lozenge-shaped grave'>> Google Drive sports new view and scan enhancements>> Researcher admits mistakes in stem cell study
 Do you know about Schwartz distribution theory? Generalized functions? Because that is what you are writing about, not traditional calculus functions. Your equation MEANS... $$\frac{1}{2\pi}\int_{-\infty}^\infty e^{i\omega x} \phi(x)\,d\omega = \phi(x)$$ for all test functions $\phi$ from an appropriate class.
 edgar thanks for your reply. It seems I've stumbled on something beyond my means. I dont know anything about Schwartz distribution theory and a quick search on the net didnt help at all. I thought the integral would be an easy calculus identity of sorts. Can you show me why the integral holds?