5. Vector Calculus

Fundamental Theorem For Line Integrals — Quiz

Test your understanding of fundamental theorem for line integrals with 5 practice questions.

Practice Questions

Question 1

Which of the following is a necessary condition for the Fundamental Theorem for Line Integrals to apply to a vector field $\mathbf{F}$?

Question 2

Suppose $\mathbf{F}(x,y) = (2x, 2y)$. What is the value of the line integral $\int_C \mathbf{F} \cdot d\mathbf{r}$ where $C$ is the curve from $(1,1)$ to $(3,4)$?

Question 3

Which of the following statements is true about a vector field $\mathbf{F}(x,y)$ if it is conservative?

Question 4

Let $\mathbf{F}(x,y,z) = (y, z, x)$. Determine if $\mathbf{F}$ is conservative and, if so, find the potential function $f(x,y,z)$.

Question 5

If $\mathbf{F}(x,y) = (3x^2 - y, x + 2y)$, what is the value of the line integral along the curve from $(0,0)$ to $(1,2)$?