Approximating Finite Sums with IntegralsIn many

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

Problem 23AAE Chapter 5

Thomas' Calculus: Early Transcendentals | 13th Edition

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Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 23AAE

Approximating Finite Sums with Integrals

In many applications of calculus, integrals are used to approximate finite sums—the reverse of the usual procedure of using finite sums to approximate integrals.

For example, let’s estimate the sum of the square roots of the first n positive integers,  The integral

is the limit of the upper sums

Therefore, when n is large, will be close to 2/3 and we will have

The following table shows how good the approximation can be.

Evaluate  by showing that the limit is  and evaluating the integral.

Step-by-Step Solution:

Step 1 of  4

We have to evaluate

Step 2 of 4</p>

=  

We know that is the limit of the upper sum

We have to find the value of the integral

Step 3 of 4

Chapter 5, Problem 23AAE is Solved
Step 4 of 4

Textbook: Thomas' Calculus: Early Transcendentals
Edition: 13th
Author: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass
ISBN: 9780321884077

This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13th. This full solution covers the following key subjects: Sums, Finite, Integrals, Limit, integral. This expansive textbook survival guide covers 138 chapters, and 9198 solutions. Thomas' Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321884077. The full step-by-step solution to problem: 23AAE from chapter: 5 was answered by Sieva Kozinsky, our top Calculus solution expert on 08/01/17, 02:37PM. Since the solution to 23AAE from 5 chapter was answered, more than 226 students have viewed the full step-by-step answer. The answer to “Approximating Finite Sums with IntegralsIn many applications of calculus, integrals are used to approximate finite sums—the reverse of the usual procedure of using finite sums to approximate integrals.For example, let’s estimate the sum of the square roots of the first n positive integers, The integral is the limit of the upper sums Therefore, when n is large, will be close to 2/3 and we will have The following table shows how good the approximation can be. Evaluate by showing that the limit is and evaluating the integral.” is broken down into a number of easy to follow steps, and 87 words.

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