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Math Help - MVT for Int.

  1. #1
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    May 2009
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    MVT for Int.

    How do I prove the mean value theorem for integrals for a constant function.
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  2. #2
    Super Member Gamma's Avatar
    Joined
    Dec 2008
    From
    Iowa City, IA
    Posts
    517
    For a constant function f(x)=c

    You want to show that there is a value z in [a,b] such that

    f(z)=\frac{1}{b-a}\int_a^bcdx=\frac{1}{b-a}c[b-a]=c
    So it turns out you can just pick any point in [a,b] and it will have this property.
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