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: 5

Answer

Let $\textbf{r}(t) = f(t) \textbf{i} + g(t) \textbf{j} + h(t) \textbf{k}$ $\int \textbf{r}(t) dt = \langle \int f(t) dt, \int g(t) dt , \int h(t) dt \rangle + \textbf{C}$

Work Step by Step

Definition of Indefinite Integral of a Vector-Valued Function (See page 813). To find the integral of $\textbf{r}(t)$, integrate each component of $\textbf{r}(t)$.
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