= (b) Suppose f(x) > 0 for any & € [a,b]. Suppose [ f(x) dx = 0. Prove that ſºg()f(x) dx = 0. Hint: use the fact that th

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B Suppose F X 0 For Any A B Suppose F X Dx 0 Prove That Sog F X Dx 0 Hint Use The Fact That Th 1 (48.08 KiB) Viewed 18 times

= (b) Suppose f(x) > 0 for any & € [a,b]. Suppose [ f(x) dx = 0. Prove that ſºg()f(x) dx = 0. Hint: use the fact that there exist m, M ER such that m 5 g(x) < M for all x € [a,b]. S* f(z) de # 0. Prove that there exists c € [a, b] S® 9(2)f(x) dx = 9(e) [° r(2) dx. de (c) Suppose f(x) > 0 for any x e [a, b] and ob such that =