三重积分变换公式的证明  

Demonstration of transformation formulae of triple integral

作　　者：刘慧钦[1] 蒋婷[2] 

机构地区：[1]烟台教育学院数学系,烟台264001 [2]长春工程学院基础部,长春130012

出　　处：《长春工程学院学报（自然科学版）》2004年第2期59-60,66,共3页Journal of Changchun Institute of Technology：Natural Sciences Edition

摘　　要：由于部分三重积分在直角坐标系下计算比较困难 ,选择适当的坐标变换 ,使得原坐标下积分区域变换为新坐标系下积分区域 ,新坐标系下积分面正交。从而各函数在满足一定条件下 ,证明了积分转换公式的成立。并通过实例验证公式的正确性。It is rather difficult to calculate some triple integral in rectangular coordinates. By using suitable coordinate transferring, the integral region in the original coordinates can be transferred into integral region in the new coordinates, and the integral plates in the new coordinates intersect orthogonally. Calculation result proves that the transferring formulae of triple integral are correct, if all the functions meet certain condition.

关 键 词：三重积分 坐标变换 积分区域 

分 类 号：O172[理学—数学]