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5.9.10  The Dirac distribution: Dirac

The Dirac command takes as input a number.
Dirac returns infinity if the number is 0, it returns 0 otherwise.

Dirac represents the distribution which is the derivative of the Heaviside function. This means that



−∞
 Dirac(xdx = 1

and, in fact, ∫ab Dirac(x) dx is 1 if [a,b] contains 0 and the integral is 0 otherwise. The defining property of the Dirac distribution is that



−∞
 Dirac(xf(xdx = f(0)

and consequently

b


a
 Dirac(xcf(xdx = f(c)

as long as c is in [a,b].
Input:

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

Output:

sin(0)

Input:

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

Output:

sin(1)

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