Lecture
Fundamental Theorem of Calculus Example
Description
This lecture illustrates the importance of the fundamental theorem of calculus by providing an example with the function F(x) = x² over the closed interval [0,1]. It demonstrates the process of calculating primitives of continuous functions and emphasizes the practical significance of the theorem in computing these primitives. Through a detailed explanation and visual aids, the instructor shows how to calculate the integral of F(x) using a regular partition of the interval, leading to the conclusion that the primitive function G(x) = (1/3)x³. The lecture concludes by establishing the continuity and differentiability of G(x) on the closed interval [0,1], highlighting its classification as a C1 function.
In MOOCs (9)
Analyse I
Le contenu de ce cours correspond à celui du cours d'Analyse I, comme il est enseigné pour les étudiantes et les étudiants de l'EPFL pendant leur premier semestre. Chaque chapitre du cours correspond
Analyse I (partie 1) : Prélude, notions de base, les nombres réels
Concepts de base de l'analyse réelle et introduction aux nombres réels.
Analyse I (partie 2) : Introduction aux nombres complexes
Introduction aux nombres complexes
Analyse I (partie 3) : Suites de nombres réels I et II
Suites de nombres réels.
Analyse I (partie 4) : Limite d'une fonction, fonctions continues
Limite d’une fonction et fonctions continues
Official source
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Ontological neighbourhood
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