Calculation of double integral by Green's theorem
GONG Xingtian
YANG Shuwei
Abstract：The calculation of double integrals has always been one of the core contents of higher mathematics teaching.Based on the homogeneity of the integrand,combined with Green's theorem,the calculation formula for converting double integrals on a closed domain into curve integrals on the boundary and its special cases are provided.Transforming double integrals into single integrals,dimensionality reduction makes calculations more convenient and simplified;On the other hand,this conclusion provides a new way to calculate double integrals,especially for solving some difficult or complex double integrals that are difficult to solve using conventional methods,which makes this method more advantageous.Finally,the effectiveness of the theory is confirmed through some typical examples.
Keywords：double integralGreen's theoremcurve integralhomogeneous function
Publication Date：2023-12-15
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：5( 338-342 )