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.
int(Dirac(x)*sin(x),x,-1,2) |
|
int(Dirac(x-1)*sin(x),x,-1,2) |
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