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Integral mean value theorem

  1. Jun 14, 2009 #1

    Take a look at the Wikipedia proof. Now, wouldn't it be easier to prove it like this:
    The ordinary mean value theorem says that

    And the fundamental theorem of calculus says that
    G(b)-G(a)=\int_a^b G'(x)dx

    So the conclusion is
    \int_a^b G'(x)dx=(b-a)G'(\xi)
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Jun 15, 2009 #2


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    You proved the case where [tex] \phi = 1[/tex] identically. Notice the wikipedia proof covers a far broader case than you did.

    Also, you probably used the mean value theorem to prove the fundamental theorem of calculus, so this is circular
  4. Jun 15, 2009 #3
    I see.
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