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[✓] Understand the function t*DiracDelta[t] at t=0 - Strange result?

GROUPS:

Hello everyone. I defined the "function":

f[t_] := t DiracDelta[t]

If I write f[0], the result wil be 0; this is strange because at t=0 the DiracDelta is undefined. If I plot the "function":

Plot[f[t], {t, -5, 5}]

at t=0 the "function" will be undefined (this is ok). Why f[0]=0?

Thank you in advance.

POSTED BY: Gennaro Arguzzi
Answer
3 months ago

The integral of the delta function is 1. Multiplying that by 0 gives 0, so the integral of t*delta(t) is 0. Since it's >=0, it's 0.

POSTED BY: Frank Kampas
Answer
3 months ago

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