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DECOMPOSITION OF A DEFINITE INTEGRAL INTO SEVERAL OTHERS. IMAGINARY DEFINITE INTEGRALS. GEOMETRIC REPRESENTATION OF REAL DEFINITE INTEGRALS. DECOMPOSITION OF THE FUNCTION UNDER THE \(\int \) SIGN INTO TWO FACTORS IN WHICH ONE ALWAYS MAINTAINS THE SAME SIGN.

  • Dennis M. CatesEmail author
Chapter

Abstract

To divide the definite integral
$$\begin{aligned} \int _{x_0}^X{f(x) dx} \end{aligned}$$
into several others of the same type, it suffices to decompose into several parts, either the function under the \(\int \) sign or the difference \( X-x_0. \ \) First, let us suppose
$$\begin{aligned} f(x)=\varphi (x)+\chi (x)+\psi (x)+\cdots . \end{aligned}$$

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sun CityUSA

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