积分的新概念  

The new concept of integral

作　　者：师教民[1] 纪敬改[2] 

机构地区：[1]石家庄职业技术学院基础部,河北石家庄050081 [2]河北晋州第一中学,河北晋州052260

出　　处：《石家庄职业技术学院学报》2001年第2期1-3,共3页Journal of Shijiazhuang College of Applied Technology

摘　　要：把积分定义为微分的无限积累 ,揭示出积分的本质就是无限个微分之和 ,将经典理论中性质不同的“定积分”、“不定积分”、“广义积分”合并成新的“积分”概念 .阐明了积分等于原函数增量以及连续与可原、连续与积分的关系 ,说明了积分的几何意义是无限个微分曲边梯形面积之和 .The definition of integral as differential unlimited accumulation reveals that the essence of integral is the sum of infinite differential.Combining“definite integral”,“indefinite integral”,“general integral”,which are not connected with one another in classic theory,into the new concept of integral illustrates the equality between integral and increment of original function,the connection of continuity and original function,continuity and integral;and also shows that the geometric meaning of integral is the area sum of infinite differential curve trapezoid.

关 键 词：原数 积微分 微分矩形 微分曲边梯形 

分 类 号：O172[理学—数学]