## Abstract

Consider that an integral relative to In this latter case, the integral in question will become what we will call a

*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 ( 19) (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$$\begin{aligned} a=\displaystyle \frac{\pm }{\infty } \ \ \ \ \ \ \ \ \text {or else} \ \ \ \ \ \ \ \ f(a)=\pm \infty . \end{aligned}$$

*singular definite integral*. It will ordinarily be easy to calculate its value with the help of formulas ( 15) and ( 16) of the twenty-third lecture, as we shall see.## Copyright information

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