极坐标变换下二重积分解法探究  

On Solution of the Double Integral via Polar Coordinate Transformation

作　　者：张群力 ZHANG Qun-li(School of Mathematical and Statistics,Heze University,Heze Shandong 274015,China)

机构地区：[1]菏泽学院数学与统计学院,山东菏泽274000

出　　处：《菏泽学院学报》2024年第5期16-21,共6页Journal of Heze University

基　　金：山东省自然科学基金项目(ZR2014AM032);山东省高等学校科技计划项目(J16LI15)。

摘　　要：二重积分计算难易关键是对积分区域、被积函数表达式做适当的变换,进而利于求解过程的简化.对含有x 2+y 2的二重积分,将积分区域的曲线、被积函数分别作相应的标准化处理,然后借助极坐标变换做相应的求解,从中得知,标准化被积函数计算二重积分优于标准化积分区域计算二重积分.The key to the difficulty of double integration calculation is to make appropriate transformations to the integration region and the expression of the integrand function,which facilitates the simplification of the solving process.For double integrals containing x 2+y 2,the curves and integrands in the integration region are respectively standardized,and then solved using polar coordinate transformation.It is found that calculating double integrals using standardized integrands is better than calculating double integrals using standardized integration regions.

关 键 词：二重积分 极坐标变换 积分区域 被积函数 

分 类 号：O172.2[理学—数学]