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Integration Proof

  1. Oct 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove if f is integrable on [a,b] then [tex]\exists c[/tex] [tex] a\leq c \leq b[/tex] so that [tex]\int_a^cf = \int_c^bf[/tex]

    3. The attempt at a solution
    I know that you have to use the first fundamental theorem of calculus and start with:
    [tex]g(x) = \int_a^xf(t)dt-\int_x^bf(t)dt[/tex]

    I'm not sure how to get started and to use this fact to help prove it. Any help would be really appreciated. Thanks!
  2. jcsd
  3. Oct 25, 2009 #2


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    g(x) is a continuous function, right? Use the intermediate value theorem. What are g(a) and g(b)?
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