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The Dirac delta function, [tex]\delta (x)[/tex] has the property that:

(1) [tex]\int_{-\infty}^{+\infty} f(x) \delta (x) dx = f(0)[/tex]

Will this same effect happen for the following bounds on the integral:

(2) [tex]\int_{0}^{+\infty} f(x) \delta (x) dx = f(0)[/tex]

My intuition tells me that it should, but the fact that the peak of the delta function lies on one of the bounds makes me think I should double check my reasoning. So, does anyone know if (2) above is correct?

Thanks for any advice you can offer.

(1) [tex]\int_{-\infty}^{+\infty} f(x) \delta (x) dx = f(0)[/tex]

Will this same effect happen for the following bounds on the integral:

(2) [tex]\int_{0}^{+\infty} f(x) \delta (x) dx = f(0)[/tex]

My intuition tells me that it should, but the fact that the peak of the delta function lies on one of the bounds makes me think I should double check my reasoning. So, does anyone know if (2) above is correct?

Thanks for any advice you can offer.

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