Paper Title:

Antiderivatives and Integrals Involving Incomplete Beta Functions with Applications

Author(s):

R. AlAhmad^1,2 and H. Almefleh¹

Mathematics Department,
Yarmouk University,
Irbid 21163,
Jordan.
E-mail: rami_thenat@yu.edu.jo

Faculty of Engineering,
Higher Colleges of Technology,
Ras Alkhaimah,
UAE.

Abstract:

In this paper, we prove that incomplete beta functions are antiderivatives of several products and powers of trigonometric functions, we give formulas for antiderivatives for products and powers of trigonometric functions in term of incomplete beta functions, and we evaluate integrals involving trigonometric functions using incomplete beta functions. Also, we extend some properties of the beta functions to the incomplete beta functions. As an application for the above results, we find the moments for certain probability distributions.

Full Text PDF: