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 ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Dirac delta function, change of variable confusion

**Physics Forums | Science Articles, Homework Help, Discussion**