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How does Wolfram Language deal with DiracDelta[0] in Integrate command?

Posted 8 years ago

Hi,

I'm trying to compute the following integral involving derivatives of Heaviside step function, which on integration by parts gives DiracDelta[0] which is undefined or infinite.

Integrate[f[x]D[D[HeavisideTheta[x],x],x],{x,0,2}]

But Mathematica seems to be making the term containing DiracDelta[0] as zero. I have attached the Mathematica file for a clear understanding of my query. Any help is much appreciated.

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POSTED BY: Vamsi Meesala
3 Replies
POSTED BY: Vamsi Meesala
POSTED BY: Daniel Lichtblau

Integrate across the origin e.g. from -2 to 2.

Integrate[f[x] D[D[HeavisideTheta[x], x], x], {x, -2, 2}]

(* Out[5]= -Derivative[1][f][0] *)

Integrating that particular expression with 0 as an endpoint of the integration interval is in effect GIGO ("garbage in, garbage out").

POSTED BY: Daniel Lichtblau
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