Suppose I have a real function $f(x)$ that is only non-zero for $x \geq 0$. Is the integral $\int^{\infty}_{-\infty}\delta(x)f(x)dx$ defined?

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    $\begingroup$ math.stackexchange.com/questions/3723/… $\endgroup$ – user223391 Mar 3 '17 at 14:05
  • $\begingroup$ Thanks! A relevant question: is the integral still defined if the delta function is replaced with the Dirac unit doublet $\delta'(x)$? $\endgroup$ – David Young Mar 3 '17 at 15:03

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