Calculus (3rd Edition)

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

Chapter 5 - The Integral - 5.2 The Definite Integral - Exercises - Page 246: 75


$$\int_{0}^{1} x^{5} d x \leq \int_{0}^{1} x^{4} d x$$ $$ \int_{1}^{2} x^{4} d x \leq \int_{1}^{2} x^{5} d x $$

Work Step by Step

Since $x^{5} \leq x^{4},$ for $x\in [0,1] $, then $$\int_{0}^{1} x^{5} d x \leq \int_{0}^{1} x^{4} d x$$ and $x^{4} \leq x^{5}$ for $x \in[1,2]$, then $$ \int_{1}^{2} x^{4} d x \leq \int_{1}^{2} x^{5} d x $$
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.