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6. Let a < b and let f : [a, b] → R be continuous. (a)...

6. Let a < b and let f : [a, b] → R be continuous. (a) Prove that if there exists an x0 ∈ [a, b] for which f(x0) 6= 0, then Z b a |f(x)|dxL > 0. (b) Use (a) to conclude that if Z b a |f(x)|dx = 0, then f(x) := 0 for all x ∈ [a, b].

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