Suppose that the closed region D is surrounded by piecewise smooth curves, and the sum of functions has a first-order continuous partial derivative on D, then there is, where L is the boundary curve in which D takes the positive direction.

2. The positive direction of the boundary closed curve L of the plane area D is defined as: if a person walks along L, the proximal part of D is always on his left, then the person's forward direction is the positive direction of L (so the outer side is counterclockwise and the inner side is clockwise).

3. Apply Green's formula to calculate the plane graphic area through curve integration:

In Green's formula, if we take p =-y; Q=x, if you take the dotted line as the integration path, you will get

(Actually, you don't need to recite it. You can roughly deduce the path from M0 to M 1 by looking at the picture, y=y0 (constant), so dy=0, so Q=0, leaving the product p. Similarly, M 1 to m, x=x0 (constant), so dx=0, so P=0, leaving the product.