FORMULAS FOR THE DETERMINATION OF EXACT OR APPROXIMATE VALUES OF DEFINITE INTEGRALS

Dennis M. Cates ()

Chapter Chapter 22 in Cauchy's Calcul Infinitésimal, 2019, pp 117-121 from Springer

Abstract: Abstract After what has been said in the last lecture, if we divide $$ X-x_0 $$ into infinitely small elements $$ x_1-x_0, x_2-x_1, \dots , X-x_{n-1}, $$ the sum $$ S=(x_1-x_0)f(x_0)+(x_2-x_1)f(x_1)+\cdots +(X-x_{n-1})f(x_{n-1}) $$ will converge toward a limit represented by the definite integral.

Date: 2019
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DOI: 10.1007/978-3-030-11036-9_22

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