Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises: 49

Answer

$\int\textbf{r}(t) dt = \langle 2sin(t), \frac{-2}{3}cos(3t), \frac{1}{2}sin(8t) \rangle + C$

Work Step by Step

To find the indefinite integral, compute the integral of each component. $\int\textbf{r}(t) dt = \langle \int 2cos(t)\ dt,\int 2sin(3t)\ dt,\int 4cos(8t)\ dt\rangle = \langle 2sin(t), \frac{-2}{3}cos(3t), \frac{1}{2}sin(8t) \rangle + C$
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