# Integrals and dirac delta function

1. Aug 27, 2005

### 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 sorta 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)?

Last edited: Aug 27, 2005
2. Aug 27, 2005

### CarlB

You got it right, and your analysis is correct.

Carl

3. Aug 27, 2005

### Fermat

You mean, like this

4. Aug 28, 2005

### EvLer

Thanks for checking my work and ... um... Latex (i still dunno how to do that, will have to read tutorials in Physics section).

5. Aug 28, 2005

### Fermat

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 $$\int_{-\infty}^{+\infty}$$