Question: (a) Let h{x) 0 be a continuous, non-negative function defined on an interval [a. b]. Prove that beh(x)dx = 0 if and only if

(a) Let h{x) ≥ 0 be a continuous, non-negative function defined on an interval [a. b]. Prove that ∫beh(x)dx = 0 if and only if h(x) = 0. Hint: Use the fact that ∫-di h(x)dx > 0 if h(x) > 0 for c (b) Give an example that shows that this result is not valid if h is allowed to be discontinuous.

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