12. Green’s Theorem

Applications To Area And Flow — Quiz

Test your understanding of applications to area and flow with 5 practice questions.

Read the lesson first

Practice Questions

Question 1

Which line integral formula gives the area $A$ enclosed by a positively oriented, simple closed curve $C$?

Question 2

In Green's theorem, the outward flux across a positively oriented boundary $C$ is equal to which double integral?

Question 3

If $\mathbf F=\langle P,Q\rangle$ satisfies $\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}=0$ everywhere on $D$, what is the net outward flux across any simple closed positively oriented boundary $C$ of $D$?

Question 4

Which vector field can be used with Green's theorem to compute area by $A=\oint_C P\,dx+Q\,dy$ because $\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}=1$?

Question 5

Using the area formula, what is the area enclosed by the unit circle $x^2+y^2=1$?