Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 4 - Integration - 4.6 The Fundamental Theorem Of Calculus - Exercises Set 4.6 - Page 320: 8

Answer

\[ \int_{1}^{27} x^{-\frac{2}{3}} d x=6 \]

Work Step by Step

The area below the curve $f(x)=x^{-\frac{2}{3}}$ over the interval [1,27] is $\int_{1}^{27} x^{-\frac{2}{3}} d x$ \[ \begin{aligned} \int_{1}^{27} x^{-\frac{2}{3}} d x &=\left.2 \sqrt[3]{x}\right|_{1} ^{27} \\ &=[-\sqrt[3]{1}+\sqrt[3]{27}].3 \\ &=[-1+3].3 \\ &=\left[\begin{array}{ll} 6 \end{array}\right] \end{aligned} \]
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