I am trying to solve the integral(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int_{-\infty}^\infty H(x) \delta(x) dx[/itex]

Where H(x) is a unit step and d(x) is a standard Dirac delta. Mathematica chokes on this, but I'm pretty sure that the value is

[itex]\int_{-\infty}^\infty H(x) \delta(x) dx = \dfrac12 \left(H(0^+) + H(0^-) \right) = 1/2[/itex]

However, I am having trouble proving that my intuition is correct. Is this claim correct, and, if so, how can I show it?

Thank you in advance.

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