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## Homework Statement

Prove that, if f is continuous on [a,b] and

∫

_{a}

^{b}= l f(x) l dx = zero

then f(x) = 0 for all x in [a ,b].

## Homework Equations

Hint- from book-

Section 2.4 Exercise 50

Let f and g be continuous at c. Prove that if:

(a) f(c) > o, then there exists delta > o such that f(x) > 0 for all x E (c- delta, c + delta)

(b) f(c) < o, then there exists delta > o such that f(x) < 0 for all x E (c- delta, c + delta)

(c) f(c) < g(c) , then there exists delta > o such that f(x) < g(x) for all x E (c- delta, c + delta)

## The Attempt at a Solution

I understand what we are trying to prove, I can visualize it, but I have NO idea what the "hint" has to do anything. I'm really not a "math person" I discovered. That is a terrible realization. I'm not just looking for the answer though, I just have no idea where to start and proofs scare me.