The matrix representation of a univariate function is equal to the image of the independent variable matrix representation under that function at the no fluctuation limit. In recent studies of BEBBYT group this fact is extended in such a way that the matrix representation of a univariate function can be expressed as a linear combination of the same function with two different matrix arguments each of which characterizes a deviation from the matrix representation of the independent variable when all fluctuations except the very first few are ignored. This idea urges us to search for more than two matrices whose images under the target function are combined to get better approximation. This paper focuses on the application of this approximation method on the integral representation of the Taylor series expansion. Here the basic conceptual background is given. Some illustrative implementations will be given at the relevant conference presentation.