【摘要】 引入了广义奇函数和广义偶函数的概念,指出并证明了广义奇、偶函数与奇、偶函数之间的关系.进一步给出了广义奇函数和广义偶函数的基本性质.应用奇、偶函数关于对称区间的定积分性质以及广义奇、偶函数与奇、偶函数之间的关系,给出并证明了广义奇、偶函数的定积分性质.通过实例说明,在某些定积分的计算中并不需要求出原函数,而是通过应用广义奇偶性,便可简化定积分的计算.更多还原

【Abstract】 The paper introduces the concept of generalized odd function and generalized even function and points out and proves the relationship between the generalized even and odd function and even function.Further it offers the basic properties of the generalized odd function and even function.The relationship between the generalized integral properties and the generalized parity function and odd even function application parity function on the symmetric interval are given,and the property of the definite integral of generalized odd and even functions as well.By the example,in the calculation of some definite integral is not needed to calculate the original function,but the ingenious application of the generalized parity,to simplify the integral calculation.更多还原