一道全国大学生数学竞赛试题的四种解法

Four Approaches to a Problem of National College Students' Mathematical Competition

针对2012年第四届全国大学生数学竟赛中非数学类的一道预赛题,分别利用三重积分中值定理、三重积分球(柱)坐标变换及含参变量积分的可微性,通过函数求导的不同技巧,得出4种解法.

This paper deals with a problem of the Fourth National College Students' Mathematical Competition in 2012.With the mean value theorem for triple integral,the spherical and cylindrical coordinates transformation,and the differentiability of the parametric variable integral,four approaches to the problem are illustrated.