I somehow understand "why" that works, but when it comes to prove it I fail... I managed to "half-prove" it by(adsbygoogle = window.adsbygoogle || []).push({});

saying:

∫f(x)δ(x)dx=f(a)*δ(a)+...+f(0)*δ(0)+...+f(b)*δ(b)=f(a)*0+...f(0)*1+...+f(b)*0=f(0)

note: integral goes from "a" to b", a<0, b>0 and δ(x) is Dirac-delta function

but I figured out I've missed to put Δx in every term and now it confuses me even more...

help!

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# I Prove that ∫f(x)δ(x)dx=f(0)

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