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INTEGRATION BY SERIES.

  • Dennis M. CatesEmail author
Chapter

Abstract

Consider a series whose different terms are functions of the variable x,  that remain continuous between the limits \(x=x_0, \) \(x=X. \ \) If, after having multiplied these same terms by dx,  we integrate between the limits in question, we will obtain a new series composed of the definite integrals
$$\begin{aligned} \int _{x_0}^{X}{u_0 \, dx}, \ \ \ \ \ \int _{x_0}^{X}{u_1 \, dx}, \ \ \ \ \ \ \int _{x_0}^{X}{u_2 \, dx}, \ \ \ \ \ \int _{x_0}^{X}{u_3 \, dx}, \ \ \ \ \ \dots , \ \ \ \ \ \int _{x_0}^{X}{u_n \, dx}, \ \ \ \ \ \dots . \end{aligned}$$
By comparing this new series to the first, we will establish without difficulty the theorem that we now state.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sun CityUSA

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