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Double integral laws

  1. Feb 6, 2010 #1
    [tex]\int_{0}^{\infty}fdx\int_{\frac{x-tx}{t}}^{\infty}dy=\int_{0}^{\infty}dx\int_{\frac{x-tx}{t}}^{\infty}fdy[/tex]

    f is a function of x and y

    can i move f like i showed?

    can i change the order of integration
    ?
     
    Last edited: Feb 6, 2010
  2. jcsd
  3. Feb 6, 2010 #2
    As stated, your integral does not exist because the term

    [tex]\int_{\frac{x-tx}{t}}^{\infty}dy[/tex]

    diverges. To answer your question more generally, yes, you may move f provided it is only a function of x and not of y. In that case f is a constant w.r.t. y, and you may move constants in and out of an integral. If f is a function of y, it *has* to be inside the dy integral - your left-hand integral would not make sense. By the way, I am assuming your integral is intended to be

    [tex]\int_{0}^{\infty}f(x) \left( \int_{\frac{x-tx}{t}}^{\infty}dy \right) dx [/tex]
     
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