COMPARISON OF TWO TYPES OF SIMPLE INTEGRALS WHICH RESULT IN CERTAIN CASES FROM A DOUBLE INTEGRATION

Dennis M. Cates ()

Chapter Chapter 34 in Cauchy's Calcul Infinitésimal, 2019, pp 185-190 from Springer

Abstract: Abstract Consider that equation ( 15 ) of the preceding lecture is satisfied. If we integrate this equation twice, namely once with respect to x between the limits $$x_0, X, $$ and once with respect to y between the limits $$y_0, Y, $$ we will find $$\begin{aligned} \int _{x_0}^{X}{\big [ \varphi (x, Y)-\varphi (x, y_0) \big ] \, dx}=\int _{y_0}^{Y}{\big [ \chi (X, y)-\chi (x_0, y) \big ] \, dy}. \end{aligned}$$

Date: 2019
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DOI: 10.1007/978-3-030-11036-9_34

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