学员视角下一道第二类平面曲线积分题目的解法探讨

Research on Solutions to One Second Type Curvilinear Integral in Perspective of Students

为培养学员的发散思维,针对一道第二类平面曲线积分题目的计算方法进行探讨,提出4种计算方法:可以利用格林公式计算;可以先将曲线方程代入被积函数中,再利用平面曲线积分与路径无关的性质计算;也可以先利用平面曲线积分的性质,再利用平面曲线积分与路径无关的性质计算;还可以将其直接转化成定积分计算。

Discussed the subject for a second type curvilinear integral and proposed 4 kinds of calculation methods in order to cultivate divergent thinking of the students.The four methods included applying Green formula,first using substitution method or properties of curvilinear integral and then some equivalence conditions for the curvilinear integral being independent of its integral path,and directly transforming the curvilinear integral to definite integral.