# Integral homework problems

by Apteronotus
Tags: homework, integral
 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.