The Dirac delta "function" is often given as :(adsbygoogle = window.adsbygoogle || []).push({});

δ(x) = ∞ | x [itex]=[/itex] 0

δ(x) = 0 | x [itex]\neq[/itex] 0

and ∫δ(x)f(x)dx = f(0).

What about δ(cx)? By u=cx substitution into above integral is, ∫δ(cx)f(x)dx = ∫δ(u)f(u/c)du = 1/c f(0).

But intuitively, the graph of δ(cx) is thesameas the graph of δ(x)! At x=0, cx=0 so δ(cx)=∞, and everywhere else cx[itex]\neq[/itex]0 so δ(cx)=0.

So how can it be that ∫δ(x)f(x)dx =1/c∫δ(cx)f(x)dx ?

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# Dirac delta function, change of variable confusion

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