Lintégrale

Lintégrale is a term used in mathematics to refer to the concept of integration, a fundamental operation in calculus. It is the inverse of differentiation and is used to find the area under a curve, the volume of solids, and to solve differential equations. There are two main types of integrals: indefinite integrals and definite integrals.

An indefinite integral, also known as an antiderivative, represents a family of functions whose derivative is a given function. It is denoted by the integral symbol followed by the function and 'dx', for example, $\int f(x) dx$. The result of an indefinite integral is a function plus an arbitrary constant of integration, denoted by 'C'.

A definite integral, on the other hand, evaluates the integral of a function over a specific interval, say from 'a' to 'b'. It is denoted by $\int_{a}^{b} f(x) dx$. The definite integral represents the net signed area between the function's graph and the x-axis over that interval. The calculation of a definite integral typically involves finding the antiderivative of the function and then evaluating it at the upper and lower limits of integration, subtracting the latter from the former. This process is often referred to as the Fundamental Theorem of Calculus.

Integration has widespread applications in physics, engineering, economics, and many other fields where continuous change needs to be analyzed and quantified.