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

1. Suppose f: [a,b]  is a function such that f(x)=0 for every x (a,b].
a) Let &#61541; > 0. Choose n &#61646; &#61518; such that a + 1/n < b and |f(a)|/n <&#61541;.
Let P ={a, a+1/n, b} &#61646; &#61520;([a,b]). Compute &#61525;(f,P) - &#61516;(f,P) and show that is less than &#61541;.

b) Prove that a&#61682; b f = 0.

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Partitions, Upper and Lower Sums and the Definition of the Riemann Integration are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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