The Dirac δ distribution is the distributional derivative of the Heaviside function. This means that
∫ |
| δ(x) dx = 1 |
and, in fact,
∫ |
| δ(x) dx = |
|
The defining property of the Dirac distribution is that
∫ |
| δ(x) f(x) dx = f(0) |
and consequently
∫ |
| δ(x−c)f(x) dx = f(c) |
as long as c is in [a,b].
The Dirac command represents the Dirac distribution.
Examples.
sin | ⎛ ⎝ | 0 | ⎞ ⎠ |
sin | ⎛ ⎝ | 1 | ⎞ ⎠ |
If you have Dirac compute a value: