双射线性变换视角下一般积分的对称性问题

The Symmetry of General Integrals in the View of Bijective Linear Transformation

针对高等数学课程中对称性问题,从双射变换的视角提出了刻画积分域对称性的新概念,借助新概念,研究了双射线性变换视角下一般积分的对称性,可用于简化积分计算.一般积分对称性的新视角可帮助学生加深对不同类型积分的对称性理解.

Aiming at the symmetry problem in the course of Advanced Mathematics,a new concept to describe the symmetry of the integral domain is proposed from the perspective of bijective transformation.With the help of the new concept,the symmetry of the general integral is studied in the view of bijective linear transformation,which can be used to simplify the integral calculation.A new perspective on general integral symmetry helps students deepen their understanding of the symmetry of different types of integrals.