2. Vector-Valued Functions

Integrals Of Vector Functions — Quiz

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

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Practice Questions

Question 1

What is the integral of the vector function $\mathbf{r}(t) = \langle 3t^2, 2t, 1 \rangle$ with respect to $t$?

Question 2

If $\mathbf{F}(t) = \langle \sin t, \cos t, e^t \rangle$, what is $\int \mathbf{F}(t) \, dt$?

Question 3

A particle moves along a path defined by the vector function $\mathbf{r}(t) = \langle t^2, t^3, t \rangle$. What is the displacement vector of the particle from $t = 1$ to $t = 3$?

Question 4

Given $\mathbf{r}(t) = \langle e^t, t, \ln t \rangle$, what is $\int_1^e \mathbf{r}(t) \, dt$?

Question 5

Which of the following represents the work done by the force $\mathbf{F}(t) = \langle 2t, 3t^2, 1 \rangle$ on a particle moving along the curve $\mathbf{r}(t) = \langle t, t^2, t^3 \rangle$ from $t = 0$ to $t = 2$?