# Thread: simple change of variables

1. ## simple change of variables

I'm being a bit thick

If I have the integral over a region, R

$\displaystyle \int_R d^{3}p f(p)$

and then change variables from $\displaystyle p \rightarrow -p$

Does the integral pick up an overall minus sign or not? i.e

$\displaystyle -\int_R d^{3}p f(p)$

I'm thinking not, because the modulus or the jacobian is positive?

2. Originally Posted by ppyvabw
I'm being a bit thick

If I have the integral over a region, R

$\displaystyle \int_R d^{3}p f(p)$

and then change variables from $\displaystyle p \rightarrow -p$

Does the integral pick up an overall minus sign or not? i.e

$\displaystyle -\int_R d^{3}p f(p)$

I'm thinking not, because the modulus or the jacobian is positive?
Correct, but you should have f(-p).

3. Originally Posted by ThePerfectHacker
Correct, but you should have f(-p).

lol ofcourse.

Just to be sure, correct as in it is

$\displaystyle +\int_R d^3 p f(-p)$

or

$\displaystyle -\int_R d^3 p f(-p)$

4. Oh I forgot

The region of integration has to switch also. Meaning all the point becomes negative points over the region you are integrating over.

5. Yeah, sorry, did you mean correct as in the sign in front of the transformed integral is + or -. (See previous post)

If R is over all space though, it makes no difference yeah?