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Math Help - simple change of variables

  1. #1
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    simple change of variables

    I'm being a bit thick

    If I have the integral over a region, R

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

    and then change variables from p \rightarrow -p

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

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

    I'm thinking not, because the modulus or the jacobian is positive?
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  2. #2
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    Quote Originally Posted by ppyvabw View Post
    I'm being a bit thick

    If I have the integral over a region, R

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

    and then change variables from p \rightarrow -p

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

    -\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).
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    Correct, but you should have f(-p).

    lol ofcourse.


    Just to be sure, correct as in it is

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

    or

    -\int_R d^3 p f(-p)
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  4. #4
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    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.
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  5. #5
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    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?
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