/sci/ - Science & Math

When taking [math]\int\delta(t-t_o) s(t)dt[/math] The answer I expect is s(t_0) but then when I use wolfram alpha to compute [math]\int_0^2\{pi R}\delta(t-t_o) e^{frac{-ikx}{R}}dt[/math] I get a function that relies on heavyside functions. Does chaning the limits of integration change the way delta works in an integral?