Intégration

Intégration is a term used across disciplines to denote the act or process of combining parts into a unified whole. In mathematics, calculus, integration is the process of determining an integral, representing accumulation, area, or probability. An indefinite integral yields a family of antiderivatives, while a definite integral assigns a numerical value to the accumulation over a specified interval. The Fundamental Theorem of Calculus links differentiation and integration. Common techniques include substitution, integration by parts, partial fractions, and numerical methods when an antiderivative is not expressible in elementary functions.

In social sciences, integration refers to the process by which individuals or groups become integrated into a broader society, economy, or polity. It can involve language learning, access to education and employment, civic participation, and social networks. Integration policies aim to reduce barriers and promote equal rights, while balancing cultural identity. Measurement of social integration uses indicators such as participation rates, social cohesion, and economic independence. Debates separate integration from assimilation and multiculturalism, emphasizing coordination, inclusion, and non-discrimination.

In information technology and engineering, system and data integration describe methods to combine diverse subsystems or data sources into a coherent, interoperable whole. Data integration aligns information from multiple databases; system integration ensures components, software, and services communicate effectively. Approaches include middleware, application programming interfaces (APIs), services-oriented architectures, and standards for data formats. Benefits include streamlined operations, improved analytics, and flexibility; challenges include data quality, governance, and security.