Calculus 8th Edition

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

Chapter 4 - Integrals - 4.3 The Fundamental Theorem of Calculus - 4.3 Exercises: 24

Answer

3

Work Step by Step

Evaluate the integral: $\int^8_1 (x^{-\frac{2}{3}}) dx$ Recall the 2nd part of the Fundamental Theorem of Calculus: $\int_a^bf(x)dx = F(b) - F(a)$ Find $F(x)$: $F(x) =\int^8_1 (x^{-\frac{2}{3}}) dx$ $F(x) = \frac{3}{1}x^{\frac{1}{3}}$ $F(x) = 3\sqrt[3] x$ Now evaluate $F(b) - F(a)$: $F(8) - F(1)$ $3\sqrt[3] 8 -3\sqrt[3] 1$ $3(2) - 3(1)$ $6-3 = 3$
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.