integrare

Integrare is an Italian verb meaning to make whole, to combine parts into a larger whole, or to incorporate something into a system. It is widely used in everyday language as well as in specialized fields. The noun integrazione denotes the process or result of integration. The term derives from Latin integer, meaning whole, and is cognate with the English verb to integrate.

In mathematics, integrare refers to calculating an integral of a function, either an indefinite integral (primitiva) or a definite integral. It is a central operation in integral calculus and is linked to the fundamental theorem of calculus. In numerical analysis, integrazione numerica provides approximate values of definite integrals using methods such as the trapezoidal rule or Simpson's rule.

In information technology and data management, integrare denotes combining systems, software, or data sources into a cohesive whole. This includes system integration, data integration, and, in software development, integrazione continua (continuous integration), an automated process that builds, tests, and validates code changes.

In social and organizational contexts, integrare describes the process of including individuals or groups within a community or institution. The related integrazione is used for social integration, educational inclusion, and workplace inclusion, referring to measures that promote participation of immigrants, students with disabilities, or new employees.