We all know:
$$\int_0^\infty \delta(y) dy = 1.$$
How about
$$\int_{-\infty}^\infty y\delta(y) dy .$$
The solution of this is $0$. I have no idea how to get this.
thx,
2026-04-03 04:23:08.1775190188
Variation of Delta function integrated
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That's the definition only. In general it is
$$\int_{-\infty}^\infty f(y) \delta (y)dy = f(0)$$
Now put $f(y) = y$.