9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Integrating Vector-valued Functions — Quiz

Test your understanding of integrating vector-valued functions with 5 practice questions.

Practice Questions

Question 1

If $\mathbf{F}(t)=\langle 3t^2,4e^t\rangle$, which vector-valued function is an antiderivative of $\mathbf{F}(t)$?

Question 2

Evaluate $\int_0^1 \langle 2t,3\rangle\,dt$.

Question 3

A particle has velocity $\mathbf{v}(t)=\langle 5,2t\rangle$. What is the displacement on the interval $0\le t\le 2$?

Question 4

A particle has velocity $\mathbf{v}(t)=\langle 2t,-4\rangle$ and position $\mathbf{r}(0)=\langle 1,5\rangle$. What is $\mathbf{r}(3)$?

Question 5

Evaluate $\int_1^2 \langle e^t,t^2\rangle\,dt$.