Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises - Page 814: 6

Let $\textbf{r}(t) = \langle f(t), g(t), h(t)\rangle$ $\int_a^b \textbf{r}(t) dt = \langle \int_a^b f(t)dt, \int_a^b g(t)dt, \int_a^b h(t)dt\rangle$

Definition of Definite Integral of a Vector-Valued Function (See Page 814). To find the definite integral of $\textbf{r}(t)$, compute the definite integral of all the components of $\textbf{r}(t)$.