(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The original question required me to show that for f(x) >= 0 for all x, f continuous, where the integral (from a to b) of f =0, that f(x) = 0 for all x in [a,b]. I did that, using a proof by contradiction.

Second part of the question requires me to show that the two hypotheses (f(x) being >= 0 and f being continuous) were required.

2. Relevant equations

3. The attempt at a solution

I think counterexamples would show this, but can't figure out what would make a counterexample. Do I need to take f(x)<0 for f continuous and show that its integral can't equal zero? Similarly, take f(x)>=0 but not continuous and show that its integral also can't equal zero?

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# Homework Help: Counterexamples needed for integration question

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