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# SINGULAR DEFINITE INTEGRALS.

Chapter

## Abstract

Consider that an integral relative to x,  and in which the function under the $$\int$$ sign is denoted by f(x),  is taken between two limits infinitely close to a definite particular value a attributed to the variable $$x. \$$ If this value a is a finite quantity, and if the function f(x) remains finite and continuous in the neighborhood of $$x=a,$$ then, by virtue of formula () (twenty-second lecture), the proposed integral will be essentially null. But, it can obtain a finite value different from zero or even an infinite value, if we have
\begin{aligned} a=\displaystyle \frac{\pm }{\infty } \ \ \ \ \ \ \ \ \text {or else} \ \ \ \ \ \ \ \ f(a)=\pm \infty . \end{aligned}
In this latter case, the integral in question will become what we will call a singular definite integral. It will ordinarily be easy to calculate its value with the help of formulas () and () of the twenty-third lecture, as we shall see.

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© Springer Nature Switzerland AG 2019

## Authors and Affiliations

1. 1.Sun CityUSA