Approximate solution of integral by taylor expansion method

Abstract

In this paper we translate some functions where have the ability of differentiation infinity of time and difficult finding integration to them or their integral take long time to solve, therefore we thought by taylor series which essentially depends on differentiation.
We integrated this function definite integral founded the nearly integral after make a cutting in series, then integrate the the function of two variable twice definite integral to find the nearly integral after make a cutting in series and gave some examples, after that, we proved the uniqueness of the reminder of the series.
Last, we showed the shape of these functions using matlab program.