Green's Theorem
A 2D vector calculus theorem relating a line integral around a simple closed curve C to a double area integral over the enclosed plane region D.
Governing formula
∮_C (L dx + M dy) = ∬_D ((∂M/∂x) - (∂L/∂y)) dx dy
SI unit
2D Vector Integral Theorem
In depth
Serves as the 2D planar version of Stokes' theorem, converting boundary line integrals into interior area integrals.
Examples in the real world
Calculating two-dimensional planar area A = ½ ∮ (x dy - y dx) using line boundary integration.