关键词: Green公式, 齐次函数, 二重积分, 曲线积分

Abstract: Using Green’s theorem, a new theorem and formula are proposed and proved to convert the double integral into the curve integral with the help of a homogeneous function, which not only reflects the advantage of dimensionality reduction to a certain extent, but also provides a new way of solving double integrals. The typical examples demonstrate the ingenious use of the theory in simplifying the integral calculation.

Key words: Green’s theorem, homogeneous function, double integral, curve integral