Order the steps to apply Green's theorem ∮_C (P dx + Q dy) = ∬_D (∂ Q/∂ x − ∂ P/∂ y) dA.

Verify C is a simple, closed, positively oriented curve → Identify P and Q from the line integral → Compute ∂ Q/∂ x − ∂ P/∂ y → Set up ∬_D (∂ Q/∂ x − ∂ P/∂ y) dA → Evaluate the double integral

Physics I / Green's Theorem

Practice question · Put in order

Order the steps to apply Green's theorem ∮_C (P dx + Q dy) = ∬_D ( $\partial Q/\partial x$ − $\partial P/\partial y$ ) dA.

Set up ∬_D ( $\partial Q/\partial x$ − $\partial P/\partial y$ ) dA
Identify P and Q from the line integral
Evaluate the double integral
Compute $\partial Q/\partial x$ − $\partial P/\partial y$
Verify C is a simple, closed, positively oriented curve

Hints

Identify the two component functions before differentiating anything.
The double integral is set up only after the integrand is formed.

Show the answer

Verify C is a simple, closed, positively oriented curve
Identify P and Q from the line integral
Compute $\partial Q/\partial x$ − $\partial P/\partial y$
Set up ∬_D ( $\partial Q/\partial x$ − $\partial P/\partial y$ ) dA
Evaluate the double integral

Why

Green's theorem converts a line integral to a double integral.

Read the lesson: Green's Theorem →

Practise Green's Theorem

The app has 8 more questions on this lesson, and keeps your place in the course. Physics I is free to start.

Start Physics I free Get it onGoogle Play

Order the steps to apply Green's theorem ∮_C (P dx + Q dy) = ∬_D (∂Q/∂x\partial Q/\partial x∂Q/∂x − ∂P/∂y\partial P/\partial y∂P/∂y) dA.

Practise Green's Theorem

More questions on Green's Theorem

Order the steps to apply Green's theorem ∮_C (P dx + Q dy) = ∬_D ( $\partial Q/\partial x$ − $\partial P/\partial y$ ) dA.