Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises - Page 814: 5

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

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