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: 48

Answer

$\int\textbf{r}(t) dt = \langle \frac{-5}{3}t^{-3}-\frac{1}{3}t^3, \frac{1}{7}t^7-t^4, 2\ ln|t|\rangle + C$

Work Step by Step

To find the indefinite integral, compute the integral of each component. $\int\textbf{r}(t) dt = \langle \int 5t^{-4} - t^2\ dt,\int t^6-4t^3\ dt,\int ,2/t\ dt\rangle = \langle \frac{-5}{3}t^{-3}-\frac{1}{3}t^3, \frac{1}{7}t^7-t^4, 2\ ln|t|\rangle + C$
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