Let f : [a, b] → R be integrable. Prove there there exists a point c ∈ [a, b] such that ∫c a f(t) dt = ∫b c f(t) dt = 1
Posted: Wed May 11, 2022 10:40 pm
Let f : [a, b] → R be integrable. Prove there there exists a
point c ∈ [a, b] such that ∫c a f(t) dt = ∫b c f(t) dt = 1/2
∫b a f(t) dt. (Hint: Use F(x) = ∫x a f(t) dt for x ∈ [a, b].)
(20 marks) Let f : [a, b] → R be integrable. Prove there there exists a point ce [a, b] such that 1 f(t) dt = f(t) dt a Is it = "90) dx = } *** " sce) dt. (Hint: Use F(x) = { s(t) dt for € (a, b.) - 2) fx ) a
point c ∈ [a, b] such that ∫c a f(t) dt = ∫b c f(t) dt = 1/2
∫b a f(t) dt. (Hint: Use F(x) = ∫x a f(t) dt for x ∈ [a, b].)
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