Integrals and dirac delta function

[EvLer]

hello again,
i have an integral to solve and not sure how to approach this:

\int f(q+T)\delta (t-q)dq

and the boundaries of integral are -inf +inf couldn't figure it out with latex.
what I know about this is that if delta function is integrated like this, it would be just the value of the function f(q) at some point. What bothers me is that f(q) is shifted to the right and I am not sure where the dirac delta function samples f(q). actually, I think I'm sort of confused...with all the variables in there q and t??
Any help is very much appreciated.

edit: my best estimation of the solution to this is f(t+T)?
not sure if that's correct, but \delta (-t) = \delta (t), so \delta (t-q) = \delta (q-t) which means that the integral = f(q + T) evaluated at q = t, i.e. value of f(t + T)?

 

[CarlB]

You got it right, and your analysis is correct.

Carl

 

[Fermat]

hello again,
i have an integral to solve and not sure how to approach this:

\int_{-\infty}^{+\infty} f(q+T)\delta (t-q)dq

and the boundaries of integral are -inf +inf couldn't figure it out with latex.
...

You mean, like this

 

[EvLer]

Thanks for checking my work and ... um... Latex (i still don't know how to do that, will have to read tutorials in Physics section).

 

[Fermat]

Thanks for checking my work and ... um... Latex (i still don't know how to do that, will have to read tutorials in Physics section).

If you click on the "quote" button at the bottom of my post, you can see the latex code I used. Or, the latex code anyone else has used.

For yourself, or for anyone esle reading, you can do subscripts and superscripts with the undescore (_) and carat (^) characters.
For example, x^2 becomes x^2 and x_2 becomes x_2.

The underscore and carat characters always operate on the next "object" following them. The object can be a single character or it can be a group of characters if they are enclosed within curly brackets - {}.
So,
\int_2^3 will give \int_2^3 while \int_{-\infty}^{+\infty} gives \int_{-\infty}^{+\infty}