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Condition of f(x,t)

  1. May 31, 2010 #1
    Hi,
    it is possible to solve the following problem, I mean give at least some conditions on f(x,t)?

    [tex]

    \int_0^{\infty}e^{-x}[f(x,t)+g(t)] xdx=g(t)

    [/tex]
     
  2. jcsd
  3. May 31, 2010 #2
    i give my solution, tell me if there's something wrong with it:

    i integrate by parts the rhs:

    [tex]

    \int_0^{\infty} e^{-x}x[f(x,t)+g(t)]dx= \int_0^{\infty} e^{-x}x f(x,t)dx+g(t) = \newline
    f(x,t)_0^{\infty} -f(x,t)+g(t)

    [/tex]

    since [tex]f(x,t)_0^{\infty}=q(t)[/tex], and rhs=g(t), it follows that

    [tex]

    f(x,t)=q(t)
    [/tex]

    and then q(t)=0
     
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