- #1
Hotsuma
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Homework Statement
Give an example of a function (necessarily discontinuous) that does not satisfy the conclusion of MVT for Integrals
Homework Equations
MVT for [tex]\int[/tex] = [tex]\frac{1}{b-a}[/tex][tex]\int ^{b}_{a}[/tex] f(x) dx
The Attempt at a Solution
So I should need one point of discontinuity on every interval that is a subset of the function's domain over [a,b] such that a<b, right?
So couldn't...
f(x) = {0 if x [tex]\leq[/tex] 1, 1 if x > 1} on the interval [0,2].
We have: [tex]\frac{1}{2-0}[/tex][tex]\int^{2}_{0}[/tex] f(x) dx = 1/2, as f(x) does not equal 1/2.
Would this work?