dintégrale

Dintégrale is not a recognized term in standard mathematical terminology. In French, the integral concept is conveyed with l’intégrale, and more specifically l’intégrale définie for the definite integral and l’intégrale indéfinie for the antiderivative. The string dintégrale can appear as a typographical error, a contraction in a nonstandard text, or as a coined name in a particular work. Because it does not denote a formal, widely accepted object, its meaning is entirely dependent on context.

When interpreted as a reference to the traditional integral, the topic covers two closely related ideas. The indefinite integral, or antiderivative, of a function f is another function F such that F′ = f. The definite integral calculates the net accumulation of f over an interval [a, b], often interpreted as the signed area between the curve y = f(x) and the x-axis. The Fundamental Theorem of Calculus ties these concepts together: differentiation and integration are inverse processes.

Notational conventions include ∫ f(x) dx for an indefinite integral, and ∫_a^b f(x) dx for a definite integral. Practical computation employs analytical methods and numerical techniques such as the trapezoidal rule, Simpson’s rule, or Gaussian quadrature, especially when antiderivatives are unavailable in closed form.

In scholarly writing, it is advisable to treat dintégrale as a potential misspelling or idiosyncratic term and to confirm the intended meaning from the author. For standard treatment, refer to l’intégrale in its indefinite and definite senses, or to related concepts like the Riemann and Lebesgue integrals.

See also: integral, calculus, definite integral, indefinite integral, Fundamental Theorem of Calculus, numerical integration.