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Dirac delta function integral

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Cujo:
I have no idea how to solve this Dirac delta function integral. So I would like some help please?  :)

ataradov:
Is delta prime in this notation a standard Dirac function, or does the prime means something here?

If it is a plain Dirac function, then it would be exp(5*0). In general an integral from a to b of f(x)*delta(x-c) is f(c) for a < c < b, 1/2*f(c) if c == a or c == b, or 0 otherwise.

Cujo:

--- Quote from: ataradov on March 21, 2021, 04:39:10 am ---Is delta prime in this notation a standard Dirac function, or does the prime means something here?

If it is a plain Dirac function, then it would be exp(5*0). In general an integral from a to b of f(x)*delta(x-c) is f(c) for a < c < b, 1/2*f(c) if c == a or c == b, or 0 otherwise.

--- End quote ---

I think its the derivative of the delta function? The question doesn't say. It just says solve the integrals with no context.

ataradov:
I'm not sure if it apples to the Dirac function (partially because it is not really a function), but there is a thing where int(-inf, +inf) [f(x)*g'(x)dx] = -int(-inf, +inf) [f'(x)*g(x)dx].

I'm also not sure how this translates to definite integrals. But that may be at least direction for reseach.

ejeffrey:
Huh.  I always thought the dirac delta function was non-differentiable but according to wikipedia you can define a differential distribution by integrating by parts the definition of the delta function.

https://en.wikipedia.org/wiki/Dirac_delta_function#Distributional_derivatives

If you evaluate that formula you get -5 * exp(5*t) | t=0 = -5

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