2. Vector-Valued Functions

Integrals Of Vector Functions — Quiz

Test your understanding of integrals of vector functions with 5 practice questions.

Practice Questions

Question 1

What is the integral of the vector function $\mathbf{r}(t) = \langle 3t^2, 2t, 4 \rangle$ with respect to $t$?

Question 2

For the vector function $\mathbf{r}(t) = \langle \sin t, \cos t, t^2 \rangle$, what is the integral $\int \mathbf{r}(t) \, dt$?

Question 3

If $\mathbf{r}(t) = \langle e^t, t, \ln t \rangle$, what is the integral $\int \mathbf{r}(t) \, dt$ for $t > 0$?

Question 4

A particle moves with velocity $\mathbf{v}(t) = \langle 2t, 3, 4t^2 \rangle$. If the particle's position at $t = 0$ is $\mathbf{r}(0) = \langle 1, 0, -2 \rangle$, what is the position function $\mathbf{r}(t)$?

Question 5

Let $\mathbf{F}(t) = \langle t^3, 2t, 5 \rangle$. What is the total work done by this force from $t = 0$ to $t = 2$ along a path defined by $\mathbf{r}(t) = \langle t, t^2, t^3 \rangle$?