Silly question

  1. silly question....

    are the integrals:

    [tex]\int_a^{b}dnf(t,n)[r(n+g(n] [/tex] and

    [tex]\int_a^{b}dnf(t,n)r(n)+\int_a^{b}dkf(t,k)g(k) [/tex] the same?..i know that n and k are dummy variable so we can always make the change of variable k=n or n=k inside one of the two integral...
  2. jcsd
  3. HallsofIvy

    HallsofIvy 41,264
    Staff Emeritus
    Science Advisor

    You seem to have lost a couple of right parentheses.
    If you meant:
    [tex]\int_a^{b}dnf(t,n)[r(n)+g(n)] [/tex]

    Yes, they are exactly the same.
  4. Hurkyl

    Hurkyl 15,987
    Staff Emeritus
    Science Advisor
    Gold Member

    A technicality:

    [itex]\int f + g = \int f + \int g[/itex] provided the two integrals on the right hand side exist. (Knowing the left hand side exists is not enough)
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