Let A be an open interval in R and with a, b in A where a < b. assume f : A ->R is continuous and f(x) >=0 for every x i

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answerhappygod
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Let A be an open interval in R and with a, b in A where a < b. assume f : A ->R is continuous and f(x) >=0 for every x i

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Let A be an open interval in R and with a, b in A where a <
b. assume f : A ->R is continuous and f(x) >=0 for every x in
A. There exists at least one point y in (a,b) such that f(y) is not
equal to 0.
(a) Prove intergral (a -> b) f > 0
(b) Prove there exist a point c in (a,b) such that integral
(a->c)f = 2*integral (b->c) f
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