How do I prove the mean value theorem for integrals for a constant function.

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- May 7th 2009, 10:43 PM #1

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- May 7th 2009, 11:42 PM #2
For a constant function $\displaystyle f(x)=c$

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

$\displaystyle f(z)=\frac{1}{b-a}\int_a^bcdx=\frac{1}{b-a}c[b-a]=c$

So it turns out you can just pick any point in [a,b] and it will have this property.