My answer of 1/2 is based on assumptions that diracdelta approximating functions are even functions. It is not necessary for that to be the case. I think Maple is right and
integrate(unit_step(x) * diracdelta(x), x, minf, inf) should be undefined. pw.mac get?s it wrong. Sorry for the noise, I know this subject is a headache.
pwint(unit_step(x) * pwdelta(x),x,minf,inf) gives 1/2, should be ?und. There are more cases like this which are also wrong.
Rich
From: Richard Hennessy
Sent: Saturday, April 13, 2013 9:23 PM
To: Maxima List
Subject: Re: [Maxima] DiracDelta
I used Wolfram alpha for Mathematica?s answer.
If there was a diracdelta() function in Maxima would integrate(unit_step(x)*diracdelta(x), x, minf, inf) equal 1 or 1/2? I think 1/2. Then there is the case of integrate(between(x,0,0,?closed)*diracdelta(x),x,minf,inf). Should that be zero?
FWIW. Maple help says that integrate(f(x) * diradelta(x), x, minf, inf) is only defined for functions f(x) that are smooth (infinitely differentiable) near 0.
Mathematica says 1 for the integrate[DiracDelta(x) * unitstep[x],x,-1,1] case and integrate[DiracDelta(x) * Heaviside[x],x,-1,1] is undefined.
Rich
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