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Attempt

I had attempted to do this problem by contradiction, except I did not understand how to finish the problem. I would appreciate a few helpful hints on this one.

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- Thread starter selenne431
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- #1

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Attempt

I had attempted to do this problem by contradiction, except I did not understand how to finish the problem. I would appreciate a few helpful hints on this one.

- #2

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- #3

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Suppose you have a continuous function f such that f(x) is nonnegative and the integral from a to b is 0 AND f(x) is NOT 0 everywhere on [a,b].

You should be able to run into a contradiction.

Hint: Since f is not 0, pick some c in [a,b] where f(c)>0. Let f(c) = w > 0. Then by continuity argue that for some interval around c, f(x) > w/2. Then make a rectangle under the graph.

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