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Homework Help: Derivative vs integral

  1. Feb 7, 2006 #1
    it is simple but i have some suspession about it
    when the integral and derivative of some func can commute ?
    for ex. is it possible to say
    [tex]
    \frac{{\partial ^{} }}{{\partial y^{} }}\int_a^b {f(x,y)dx} = \int_a^b {\frac{{\partial ^{} }}{{\partial y^{} }}f(x,y)dx}
    [/tex]



    or are there any condition for f(x,y) to satisfy?(?any toplogical condition other than f integrable)
     
    Last edited: Feb 7, 2006
  2. jcsd
  3. Feb 7, 2006 #2

    quasar987

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    I my book, the theorem reads: "If M(x,y) and dM/dy are continuous functions on some region R, then < what you wrote >"

    I assume it is implied that the region R contains the interval [a,b]
     
  4. Feb 8, 2006 #3
    thanks for reply
    can you give me the name/author of the book or thm itself ?
     
  5. Feb 8, 2006 #4

    benorin

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  6. Feb 8, 2006 #5

    quasar987

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    Book has no name. Written by my college professor or multivariable calculus.
     
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