Starting from the theory of differential equations, we apply the following results (for example, see Chapter 2 of Ding and Li [2], Theorem 1).

Theorem 1: Suppose the functions P (x, y) and Q(x, y) are continuous on U = (α, β) × (γ, δ) and have continuous partial derivatives? P/？ Y and? Q/？ X. If yes, the formula 1 ω = P (x, y)dx+Q(x, y)dy is correct if and only if? P/？ y =？ Q/？ X is continuous on u. In addition, type 0 distinguished as ω can be expressed as:

x y

∫ P (ξ, y)dξ+∫ Q(x0, η)dη +C, where c is a constant.

x0 y0