integració

Integració (Catalan for integration) refers to the process of combining parts into a whole. It denotes mathematical integration as well as social, economic, or technical processes that bring elements into a coherent system. The term comes from Latin integratio, from integrare, meaning to make whole.

In mathematics, integration assigns an integral to a function, yielding an antiderivative in the indefinite case or a definite value for a definite integral. It underpins area, volume, and probability calculations and is linked to differentiation by the fundamental theorem of calculus. Techniques include substitution, integration by parts, and partial fractions; numerical methods such as the trapezoidal rule approximate integrals when closed forms are unavailable.

In social and political contexts, integració refers to policies and practices that incorporate individuals or groups into a society or economy. This includes language inclusion, education, labor-market participation, and intercultural dialogue. Challenges include discrimination, unequal access to services, and cultural tensions. Success is often measured by participation, equality, and social cohesion.

Economically, integració describes the growing interconnection of markets, institutions, and policies across regions, such as trade agreements, regulatory harmonization, and currency unions. These processes aim to reduce barriers to cross-border activity and to coordinate standards.

In technology and information management, data integration and system integration combine data and software from diverse sources to enable interoperability, analytics, and unified operations. Methods include ETL (extract, transform, load), APIs, middleware, and data governance to ensure quality and security.