I am performing lots of simple calculations with dirac delta functions. It would be awesome if Mathematica could do this routine exercise for me, eliminating any possible human errors. For example, this integral:
Integrate[DiracDelta[t - a - (r^2 + (z - a)^2)^(1/2)] /
(4 Pi (r^2 + (z - a)^2)^(1/2)), {a, -Infinity, Infinity}]
Mathematica does not know how to evaluate it.
I tried using FunctionalExpand
to expand the delta-function, but in this case it does nothing. But I can easily take the integral above manually.
Maybe there is a way of evaluating such integrals automatically?