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Is this integral a convolution ?

  1. Oct 7, 2011 #1

    Mentz114

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    I'm struggling to find a function [itex]E(t)[/itex] which is the energy inside a sphere with energy density [itex]\rho(t,r)[/itex] where the radius [itex]r \equiv r(t)[/itex] is itself a function of time. This
    [tex]
    E(t) = 8\pi \int_0^{r(t)} \rho(r,t) dr
    [/tex]
    doesn't make sense, does it ? Is the thing I'm looking for some kind of convolution of r and [itex]\rho[/itex] ?
     
  2. jcsd
  3. Oct 7, 2011 #2

    HallsofIvy

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    Why do you say it doesn't make sense? It looks perfectly reasonable to me.
     
  4. Oct 7, 2011 #3

    mathman

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    You should try to be more careful in your notation. You have ρ(t,r) in one place and ρ(r,t) someplace else. More important if r is the upper limit of the integral, it should not be used as the dummy for integration.
     
  5. Oct 7, 2011 #4

    Mentz114

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    Thanks for the replies. Sorry about the sloppiness.

    Yes, I thought there was something wrong but I'm still baffled.
     
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