Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 4 - Integrals - 4.2 The Definite Integral - 4.2 Exercises - Page 318: 59

Answer

$0\leq \int_{0}^{1}x^{3}~dx \leq 1$

Work Step by Step

From the definite integral $\int_{0}^{1}x^{3}~dx$, $x$ is between $0$ and $1$. Frame the integrand $x^{3}$. $0 \leq x \leq 1$ Raise to the power of $3$ all sides of the inequality: $0^{3} \leq x^{3} \leq 1^{3}$ $0\leq x^{3} \leq 1$ Now using the property $8$ it follows: $0(1-0) \leq \int_{0}^{1}x^{3}~dx \leq 1(1-0)$ $0\leq \int_{0}^{1}x^{3}~dx \leq 1$
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.