Lecture

Definition of Indefinite Integral

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Description

This lecture covers the definition of the indefinite integral, where a primitive of a function f is a function F such that F'(x) = f(x) for all x in the interval (a, b). It also discusses the properties of primitives, emphasizing that two primitives of a given function differ by a constant. The lecture further explores the concept of the indefinite integral of f as the set of all primitives of f, providing notations and applications of this integral.

In MOOCs (2)

Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Our final theme is integration. We begin by defining the indefinite integral and the definite integral. We introduce the definite integral using Riemann sums and upper and lower sums. We define three important properties of definite integrals: the linearity of the integral, the subdivision of the domain and the monotonicity of the integral. Function integration allows us to define the mean theorem. It states that the mean of a continuous function on a segment is realized as the value of the function at a ce

Analysis I

This course covers : Part 1: Prelude, basic concepts, real numbers. Part 2: Introduction to complex numbers. Part 3: Real number sequences I and II. Part 4: Limit of a function, continuous functions. Part 5: Continuous functions and derivable functions, the derivative function. Part 6: Studies of functions, limited developments. Part 7: Indefinite and definite integrals, integration (selected chapters).

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Ontological neighbourhood

Mathematics

Analysis: Complex analysis

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