intégrons

Intégrons is the form of the French verb intégrer in the first person plural present tense, meaning “we integrate,” and it is also used as an imperative in mathematical or instructional contexts to suggest performing an integration step, as in “Intégrons …” or “Intégrons cette fonction.” The verb intégr er has several senses, including to combine parts into a whole, to include something within a system, and, in mathematics, to carry out the operation of integration.

In mathematics, the phrase Intégrons is common in textbooks and problem statements as a cue to compute an integral. It can signify either indefinite integration (finding an antiderivative) or definite integration (evaluating an integral over a specified interval), depending on the accompanying notation. For example: “Intégrons f(x) = x^2 sur l’intervalle [0,1],” which leads to the definite integral ∫_0^1 x^2 dx = 1/3.

Etymology and relation to other terms: the verb comes from the Latin integram, via integrare, and is connected to the noun intégrale and the process or result of integration. In addition to mathematical use, intégr er spans broader meanings of inclusion and combination in everyday French.

Related topics include intégration (the act or process of integrating), l’intégrale (the integral itself), and concepts such as l’intégration numérique (numerical integration) and l’intégrateur (the integrator or computing device).