Practice question · Multiple choice
A surveyor drives a GPS-equipped car once around a lake and computes the lake’s area without ever crossing the water. Which theorem makes this possible?
Hints
- Green’s theorem converts around a region into over it. Read it right-to-left.
- Choose the field cleverly (e.g. ) and the double integral becomes , pure area.
Show the answer
A. Green's theorem: a boundary integral gives the enclosed area
Why
With the right integrand, the boundary tour computes exactly the enclosed area: . Mechanical planimeters, instruments that measure any drawn region by tracing its edge, are Green’s theorem built in brass.
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.
More questions on Green's Theorem
- Which conditions are required for Green's theorem to hold?
- Order the steps to apply Green's theorem ∮_C (P dx + Q dy) = ∬_D (∂ Q/∂ x − ∂ P/∂ y) dA.
- Complete the statement of Green’s theorem.
- Green's theorem cannot be applied when the curve is traversed clockwise.
- Green’s theorem converts a line integral around a closed curve into a double integral over the region inside.…