Solution
= Solution
Repeated <integration by parts>, or the definition of the $m$th <distributional derivative>, gives
$$
\boxed{\int_{-\infty}^{\infty}f(x)\delta^{(m)}(x)\,dx=(-1)^m f^{(m)}(0).}
$$
= Solution
Repeated <integration by parts>, or the definition of the $m$th <distributional derivative>, gives
$$
\boxed{\int_{-\infty}^{\infty}f(x)\delta^{(m)}(x)\,dx=(-1)^m f^{(m)}(0).}
$$