Study on the Relation of Definite Integral and Indefinite Integral

SUN Bao-fa

doi:10.13371/j.cnki.chin.q.j.m.2014.04.007

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 4: 523 - 528

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.04.007

Study on the Relation of Definite Integral and Indefinite Integral

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Department of Computer Science and Technology, Anhui Sanlian University

SUN Bao-fa(1965-), male, native of Hefei, Anhui, an associate professor of Anhui Sanlian University, Ph.D., engages in the qualitative theory of ordinary differential equations, mathematical modeling and computer application.

Received date: 2013-01-02

Online published: 2020-11-26

Supported by

Supported by the Colleges and Universities Provincial Scientific Research Project of Anhui Province(KJ2013B090)；

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Abstract

Relation of definite integral and indefinite integral was discussed and an important result was gotten. If f（x） is bounded and has primary function, the formal definite integral \int^x_s \tilde{f}（t）dt is the indefinite integral of f（x）, where x is a self-variable, s is a parameter,\tilde{f}（x） is a function defined in（-∞, +∞）, which comes from f（x） by restriction and extension. In other words, the indefinite integral is a special form of definite integral, its lower integral limit and upper integral limit are all indefinite.

Key words： definite integral; indefinite integral; primary function

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SUN Bao-fa . Study on the Relation of Definite Integral and Indefinite Integral[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(4) : 523 -528 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.04.007

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