Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.9 Numerical Integration - Exercises - Page 458: 36


Error $(M_{20}) \leq 5.04659 \times 10^{-5}$

Work Step by Step

Error $(M_N) \leq \dfrac{k_2(b-a)^3}{24N^2}$ For, $M=20$, we have: Error $M_{20} \leq \dfrac{(1)(\dfrac{\pi}{4}-0)^3}{24(20)^2} \\ \leq \dfrac{(1)(\dfrac{\pi^3}{64})}{24(400)}\\ \leq \dfrac{\pi^3}{614400} \\\leq 5.04659 \times 10^{-5}$
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.