# Integrating delta function with a one-sided function

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?

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