Explanation Proof: The upper sum defined for n rectangles on [ a , b ] is ∑ k = 1 n f ( M k ) Δ x . Where, M k is the maximum on [ x k − 1 , x k ] . [ x k − 1 , x k ] The lower sum defined for n rectangles on [ a , b ] is ∑

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ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Question

Chapter 4.2, Problem 50P

To determine

To prove: that for any function f and interval [a,b] , the upper sum with n rectangles is greater than or equal to the lower sum with n rectangles.

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Chapter 4.2, Problem 49A

Chapter 4.2, Problem 51P

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Chapter 4 Solutions

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To prove : that for any function f and interval [ a , b ] , the upper sum with n rectangles is greater than or equal to the lower sum with n rectangles.

Solution Summary: The author explains that the upper sum of n rectangles is greater than or equal to the lower sum.

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To prove: that for any function f and interval [a,b] , the upper sum with n rectangles is greater than or equal to the lower sum with n rectangles.

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Chapter 4 Solutions