Integrals over Dirac Delta Function Representations

This Demonstration compares the integral of a test function multiplying three different representations of the Dirac delta function, , as the index is increased. For each representation, . The three representations are (1) rectangle ; (2) Gaussian ; and (3) Lorentzian . The top panels show plots of , , and their product. The lower panel shows the integral of the product, , and how it approaches asymptotically as the index is increased.