# Integral homework problems

by Apteronotus
Tags: homework, integral
 Share this thread:
 P: 203 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,
 P: 607 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.
 P: 203 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?

 Related Discussions Calculus 3 Calculus & Beyond Homework 4 Calculus & Beyond Homework 4 Calculus & Beyond Homework 2 Calculus 1