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tδ(t) = 0

The answer our TA has given isn't doing it for me:

[itex]\int dt \delta(t)f(t) = (0)f(0) = 0[/itex]

I'm wanting to write:

[itex] t \frac{d}{dt}\int \delta(t) dt = t \frac{d}{dt}(1) = t * 0 = 0 [/itex]

Am I right here? This doesn't make use of a test function. I'm very sloppy with proofs!

Thanks for your time!

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# Proper proof of a delta function

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