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: 46


$\left\langle\frac{3}{2}t^2, 2t^3, 9t \right\rangle.$

Work Step by Step

We have \begin{align} \int_{0}^{t}\left\langle 3s, 6s^2, 9 \right\rangle ds &=\left\langle \frac{3}{2}s^2, 2s^3, 9s \right\rangle|_{0}^{t}\\ &=\left\langle \frac{3}{2}t^2, 2t^3, 9t \right\rangle-\left\langle 0, 0 ,0 \right\rangle\\ &=\left\langle\frac{3}{2}t^2, 2t^3, 9t \right\rangle. \end{align}
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