Academic Journal of Mathematical Sciences, 2023, 4(5); doi: 10.25236/AJMS.2023.040510.
Jing Zhang1, Shitong Yuan2
1Changzhi University, Changzhi, 046011, China
2School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, China
The integration of curves of type II is an important part of integrals. This paper summarizes four methods of solving the integration of curves of type II, which are the transformation of the integration of curves of type I, definite integration, dual integration, and single connection, and explains in detail the intrinsic connection and scope of application between them. The transformation of the integration of curves of type I applies to all plane curves, Green's formula requires the construction of closed curves for solving. The definite integral method requires plane curves expressed as parametric equations to be solved. The single connectivity method solves plane curves that satisfy the condition that curve integrals are independent of paths. Finally, the four solution methods are applied with examples.
Integrals of curves of type I, integrals of curves of type II, definite integrals, dual integrals
Jing Zhang, Shitong Yuan. An analysis of the solution of the integration of curves of type II. Academic Journal of Mathematical Sciences (2023) Vol. 4, Issue 5: 74-80. https://doi.org/10.25236/AJMS.2023.040510.
[1] Du Zhongming,Wan Meng,Hong Dunhua.Discussion on the separate teaching method of expression and calculation method of work in college physics course [J].Journal of Qingyuan Vocational and Technical College,2023,16(02):74-77.
[2] WU Wenxiang,Chen Shunchao,Chen Jie et al.Research on Calculation of normal section bearing capacity of Reinforced concrete rectangular beams [J].Henan Science and Technology,2022,41(23):77-81.
[3] Chen Guo-Guo.Research on dynamic frequency measurement Algorithm and low frequency load reduction scheme of power system [D].Lanzhou university of technology,2023.
[4] MA Wenshan.Application of definite integral and double integral in area calculation [J].Journal of West Fujian Vocational and Technical College,2022,24(02):116-120.
[5] Meng Xianqing,Gao Xiaoyan.Discussion on calculation of curve integral [J]. Journal of Shanxi Datong University (Natural Science Edition),2017,33(06):12-13+15.
[6] Bini D , Falanga M , Geralico A ,et al.The signal from an emitting source moving in a Schwarzschild spacetime under the influence of a radiation field[J].Classical & Quantum Gravity, 2014, 29(6):65014-65029(16).DOI:10.1088/0264-9381/29/6/065014.
[7] Koch E , Stilkerieg B , Carlsen L .Problems of the Kinetic Evaluation of DTA Curves and Non-Isothermal Rate Curves of One-Step Reactions in Solution[J].Ztschrift fr Elektrochemie, Berichte der Bunsengesellschaft fr physikalische Chemie, 2010, 83(12):1238-1245.DOI:10.1002/bbpc.19790831206.