Integreren

Integreren is a Dutch verb meaning to integrate, to combine into a whole, or to fit into a larger system. In mathematics and related sciences, integreren refers to the process of calculating an integral, which can represent area, accumulated quantities, or other continuous sums. In everyday language, it can also mean the process of joining a person or group into a community, or the integration of different parts into a larger system, for example software or hardware components.

In calculus, the integral is the reverse operation of differentiation. An indefinite integral (antiderivative) F(x) satisfies F'(x) = f(x). A definite integral ∫_a^b f(x) dx gives the net accumulation over [a,b], interpreted as area under the curve, among others. The fundamental theorem of calculus links differentiation and integration. Methods include substitution, integration by parts, partial fractions, trigonometric integrals, and numerical methods like the trapezoidal rule, Simpson's rule, or Gaussian quadrature.

System integration: In computing and engineering, integreren describes the process of combining subsystems into a complete system, ensuring interoperability. In statistics and physics, integrals appear in probability distributions, expected values, and physical quantities like work.

In social policy, integration refers to the process of including individuals or groups into society, ensuring equal access to rights and participation. Factors include language skills, education, employment, housing, social networks, and attitudes. Approaches include inclusive education, anti-discrimination measures, and integration policies in labor markets, housing, and media representation. Metrics include employment rates, educational attainment, language proficiency, and social participation.