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Riemann sum

Suppose f(x) is defined on the interval [a,b].

Let a = x0 < x1 < x2 < · · · < xn = b be n + 1 points and let $x_{i}^{\ast }$ be a point in the subinterval [xi-1,xi]  for i = 1, 2, ... , n.

Then the sum MATHis called a Riemann sum.

It is an approximation to the integral $\int_{a}^{b}f(x)dx$.


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


Left sum, right sum, middle sum

Lower sum, upper sum


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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