# Advance Calculus Riemann Integration Concepts : Partitions, Upper and Lower Sums and Definition of the Riemann Integration

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1. Suppose f: [a,b]  is a function such that f(x)=0 for every x (a,b].

a) Let  > 0. Choose n   such that a + 1/n < b and |f(a)|/n <.

Let P ={a, a+1/n, b}  ([a,b]). Compute (f,P) - (f,P) and show that is less than .

b) Prove that a b f = 0.

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