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. Cates ()

Chapter Chapter 23 in Cauchy's Calcul Infinitésimal, 2019, pp 123-127 from Springer

Abstract: 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 $$\begin{aligned} f(x)=\varphi (x)+\chi (x)+\psi (x)+\cdots . \end{aligned}$$

Date: 2019
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DOI: 10.1007/978-3-030-11036-9_23

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