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: 41


$ \left\langle 0,0\right\rangle.$

Work Step by Step

We can write \begin{align} \int_{-2}^{2}\left\langle u^3,u^5\right\rangle du&=\left\langle \frac{1}{4}u^4, \frac{1}{6}u^6\right\rangle|_{-2}^{2}\\ &=\left\langle4, \frac{64}{6}\right\rangle-\left\langle 4, \frac{64}{6}\right\rangle\\ &= \left\langle 0,0\right\rangle. \end{align}
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