Condition: 1. Region d must be simply connected, that is, region d is continuous. Generally speaking, there is no "hole" in area D;
2. The curve that constitutes area D must be continuous;
3. Curve L (which can be composed of line segments) has positive adjustment;
Conclusion: The double integral on the plane closed domain D can be expressed by the curve integral along the boundary curve L of the closed domain D; In other words, the curve integral of a closed path can be calculated by double integral. If the area D does not meet the above conditions, that is, when the intersection of the straight line passing through the area and parallel to the coordinate axis and the boundary curve exceeds two points, one or several auxiliary curves can be introduced into the area to divide it into several local areas, so that each local area is suitable for the above conditions, and Green's formula can still be proved.
Green's formula is a mathematical formula, which describes the close relationship between the curve integral of coordinates along the closed curve L on the plane and the double integral on the closed area D surrounded by the curve L. For the complex connected area D, the right end of Green's formula should include the curve integrals along all the boundaries of the area D, and the boundary direction is positive for the area D. ..
Green's formula relates the double integral with the curve integral of coordinates, so it is widely used.