Calculus (3rd Edition)

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

Chapter 14 - Calculus of Vector-Valued Functions - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 44


$\left\langle1, \frac{7}{3}, \frac{15}{4}\right\rangle.$

Work Step by Step

We can write \begin{align} \int_{1/2}^{1}\left\langle \frac{1}{ u^2},\frac{1}{ u^4},\frac{1}{ u^5}\right\rangle du&=\left\langle- \frac{1}{ u},-\frac{1}{ 3u^3},-\frac{1}{4 u^4}\right\rangle|_{1/2}^{1}\\ &\left\langle-1,-\frac{1}{ 3 },-\frac{1}{4 }\right\rangle-\left\langle- 2,-\frac{8}{ 3},-4\right\rangle\\ &= \left\langle1, \frac{7}{3}, \frac{15}{4}\right\rangle. \end{align}
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