An Algebraic Method for Solving a Class of Indefinite Integrals

DOI

10.2991/icssr-14.2014.30How to use a DOI?

Keywords

Indefinite integral, Linear space, Derivative operator, Basis function, Inverse transformation

Abstract

In this paper, an algebraic method for solving indefinite integrals of a class of functions is proposed. The essence of the method is to construct a linear space spanned by the class of functions; thus, the derivative operator is a linear transformation of the linear space. By calculating the value of the derivative operator on the basis function, the matrix of the derivative operator is obtained, and the inverse matrix is derived: this is the matrix of the inverse transformation for the derivative operator. If a function is expressed as a linear combination on the basis of the constructed linear space, one of its primitive functions can be simply represented by using the above inverse transformation. Finally, the indefinite integral of the function is obtained by adding an integral constant to the primitive function. The salient feature of this paper is to avoid the relatively complex integral calculation.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Fucheng Liao
AU  - Xiao Wang
AU  - Xuejin Yan
AU  - Di Wang
PY  - 2014/06
DA  - 2014/06
TI  - An Algebraic Method for Solving a Class of Indefinite Integrals
BT  - Proceedings of the 3rd International Conference on Science and Social Research
PB  - Atlantis Press
SP  - 122
EP  - 126
SN  - 2352-5398
UR  - https://doi.org/10.2991/icssr-14.2014.30
DO  - 10.2991/icssr-14.2014.30
ID  - Liao2014/06
ER  -