How Does Using Dirac in a Double Integral Simplify the Integration Process?

[ooga59]

Hi,

I have a question about using the dirac function in a double integral.

Lets say you have the double integral over the two values x1 and x2:

int( int( sin(x1) * dirac(x1-x2) * sin(x2) ))

Does this just simplify to a single integral:

int( (sin(x1))^2 )



thanks!

 

[HallsofIvy]

Well, that depends. You did not write any limits of integration.
$$\int_a^b \delta(x- x1)f(x)dx$$
is equal to f(x1) IF $a\le x1\le b$ and 0 otherwise.

 

[ooga59]

The limits would be from -inf to inf. Thanks.

 

[0xDEADBEEF]

AFAIK the answer is yes. But of course that non converging integral might produce some surprises.