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