重积分的积分区域和积分微元变换法

Transformation of Integral Region and Integral Differential Element in Multiple Integrals

将重积分的换元法更名为积分区域和积分微元变换法,修正了定理中的条件,指出变换积分区域和微元的结果可以使重积分中的变限积分变成定积分,从而降低了积分难度.文中还证明了将直角坐标转换成极坐标,广义极坐标,球面坐标,柱面坐标,广义柱面坐标,虽然积分微元形状和面积均发生了变化,但积分区域不变.

The change of variable in a multiple integral is renamed as the transformation of integral region and integral differential element in multiple integrals.There is some revision for conditions in the theorem.It should be pointed out that the results of transformation of integral region and differential element can turn the variable limit integral of multiple integrals into definite integral,which reduces the difficulty of integrals indeed.It is also proved that the Cartesian coordinates can be transformed into polar coordinates,generalized polar coordinates,spherical coordinates,cylindrical coordinates,generalized cylindrical coordinates.The integral region is unchanged though the shape and area of integral differential element are changed.