Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 5 - Section 5.1 - Areas and Distances - 5.1 Exercises - Page 383: 18

Answer

$A=\lim\limits_{n \to \infty}\sum_{i=1}^n\frac{5x_i+5\ln x_i}{n}$

Work Step by Step

Using the Definition 2, $A=\lim\limits_{n \to \infty}\sum_{i=1}^nf(x_i)\Delta x$ where $\Delta x=\frac{\text{upper bound - lower bound}}{n}$ Find $\Delta x$ and simplify: $\Delta x=\frac{8-3}{n}=\frac{5}{n}$ Then, $A=\lim\limits_{n \to \infty}\sum_{i=1}^n(x_i+\ln x_i)\cdot \frac{5}{n}$ $A=\lim\limits_{n \to \infty}\sum_{i=1}^n\frac{5x_i+5\ln x_i}{n}$
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