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How to differentiate this integral?

  1. Sep 3, 2007 #1

    I have an integral

    [tex] F(x) = \int\limits_a^x f(x) d(g(x)) [/tex]

    and [tex] g(x) [/tex] may and may not be differentiable.

    How can I differentiate [tex] d(F(x)) [/tex]?

  2. jcsd
  3. Sep 4, 2007 #2


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    Staff Emeritus
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    At points where g is differentiable F'(x)= f(x)g'(x). At points where g is not differentiable F is not differentiable.
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