首都师范大学学报（自然科学版）2025，Vol.46Issue(2)：38-42,67,6.DOI:10.19789/j.1004-9398.2025.02.006
巧用边界曲线的参数方程计算二重积分
Calculating the double integrals by using parametric equations of boundary curves
摘要
Abstract
To calculate the double integral,a mapping is proposed with the rectangular region to the integral region D using the parametric equation of the boundary curve of the integral region.Then a formula is proposed and proved for converting the double integral in the cartesian coordinate system into the double integral in parametric coordinates.Finally,the generality and validity of the application of the theory are demonstrated by some examples.关键词
二重积分/边界曲线/参数方程/坐标变换Key words
double integral/boundary curves/parametric equation/coordinate transformation分类
数学引用本文复制引用
巩星田,杨树伟..巧用边界曲线的参数方程计算二重积分[J].首都师范大学学报（自然科学版）,2025,46(2):38-42,67,6.基金项目
甘肃省教育厅高等学校创新基金项目(2023B-403) （2023B-403）
