Explanation Consider the upper sum approximation for an area between the graph of a function f and the x axis on [ a , b ] must always be larger than or equal to any other type of Riemann sum approximation with n number of rectangles. For calculating upper sum, maximum height of the rectangle is considered. So, the heights used in upper sum are always greater than or equal to the heights considered in any other types of the Riemann sum

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Chapter 4.2, Problem 9C

To determine

To explain: The upper sum approximation for the area between the graph of a function f and the x axis on must always be larger than or equal to any other type of Riemann sum approximation with the same number n of rectangles.

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Chapter 4.2, Problem 8C

Chapter 4.2, Problem 10C

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