Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition

Published by Brooks Cole
ISBN 10: 1-43904-957-2
ISBN 13: 978-1-43904-957-0

Chapter 6 - Analyzing Accumulated Change: Integrals in Action - 6.1 Activities - Page 423: 16

Answer

Diverges

Work Step by Step

Let us consider that $I_n=\int_{10}^{n} (\dfrac{1}{x}-10) \ dx$ After integrating, we have: $I_n=[\ln |x|-10x]_{10}^{n} = \ln |\dfrac{n}{10}|-10(n-10)$ Now, $I=\lim\limits_{n \to \infty} I_n=\int_{10}^{\infty} (\dfrac{1}{x}-10) \ dx\\=\lim\limits_{n \to \infty} [\ln |\dfrac{n}{10}|-10(n-10)] \\=\infty$ Because the logarithm and $n$ both are unbounded. So, the limit does not exist. This means that the given integral diverges.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.