- #1
wil3
- 179
- 1
I am trying to solve the integral
[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.
[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.