5. Vector Calculus

Green’s Theorem — Quiz

Test your understanding of green’s theorem with 5 practice questions.

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Practice Questions

Question 1

Which of the following best describes Green’s Theorem?

Question 2

Green’s Theorem can be applied to which of the following types of curves?

Question 3

Given the vector field $\mathbf{F}(x, y) = (P(x,y), Q(x,y)) = (y^2, x)$, what is $\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}$?

Question 4

Which of the following is a necessary condition for applying Green’s Theorem?

Question 5

Consider the vector field $\mathbf{F}(x, y) = (2x - y, 3y + x)$. What is the double integral of $\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}$ over the region enclosed by the unit circle $x^2 + y^2 = 1$?