Question

What is Green's theorem?

Answer 1

Green's theorem gives a relationship between the line integral of a two-dimensional vector field over a closed path in the plane and the double integral over the region it encloses. The fact that the integral of a (two-dimensional) conservative field over a closed path is zero is a special case of Green's theorem.

Answer 2

About:

In mathematics, Green's theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. It is named after George Green, though its first proof is due to Bernhard Riemann[1] and is the two-dimensional special case of the more general kelvins stokes theorem.

theorem :

Let C be a positively oriented, piecewise smooth, the simple closed curve in a plane, and let D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D an I plan continuous partial derivatives there, then

where the path of integration along C anticlockwise.[2][3]

In physics, Green's theorem finds many applications. One of which is solving two-dimensional flow integrals, stating that the sum of fluid outflows from a volume is equal to the total outflow summed about an enclosing areaInIn-plane geometry, and in particular, are surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter.



remember to mark brainlest