Geodesic
Definition of the definite integral
The Teaching of Mathematics, XVI (2013) no. 1, p. 29 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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In this paper we suggest a new approach for a definition of definite integral of a real function in the first course in Mathematical Analysis. The definite integral exists if for any sequence of partitions, the upper sum and the lower sum of Darboux have the same limit. If the definite integral of a real function exists, then we can simply compute it, as a limit of a sequence of integral sums of Riemann.
Classification : 1AMS97I50 2ZDMI55
Keywords: Definite integral, upper and lower sum of Darboux, Riemann sum. 
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Nikita Shekutkovski. Definition of the definite integral. The Teaching of Mathematics, XVI (2013) no. 1, p. 29 . http://geodesic.mathdoc.fr/item/TM2_2013_XVI_1_a5/