12. Green’s Theorem

Circulation Form — Quiz

Test your understanding of circulation form with 5 practice questions.

Practice Questions

Question 1

In Green’s Theorem circulation form, what orientation is considered positive for a simple closed curve $C$?

Question 2

What integral expression is the right-hand side of Green’s Theorem in circulation form for $\mathbf{F}=\langle P,Q\rangle$ over region $D$ with boundary $C$?

Question 3

If $\mathbf{F}$ is conservative on a region containing $C$, what is the value of $\oint_C P\,dx+Q\,dy$?

Question 4

For $\mathbf{F}=\langle -y,x\rangle$ and $C$ the unit circle traversed counterclockwise, what is $\oint_C P\,dx+Q\,dy$?

Question 5

Which curve description is required in the standard circulation form of Green’s Theorem?