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: 39


$\left\langle \frac{212}{3}, 124 \right\rangle.$

Work Step by Step

We have \begin{align} \int_{-1}^{3}\left\langle 8 t^{2}-t, 6 t^{3}+t\right\rangle d t&=\left\langle \frac{8}{3} t^{3}-\frac{1}{2}t^2, \frac{6}{4} t^{4}+\frac{1}{2}t^2\right\rangle|_{-1}^{3}\\ &=\left\langle 72-\frac{9}{2}, \frac{243}{2} +\frac{9}{2}\right\rangle-\left\langle -\frac{8}{3} -\frac{1}{2}, \frac{6}{4} +\frac{1}{2} \right\rangle\\ &= \left\langle \frac{212}{3}, 124 \right\rangle. \end{align}
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