integrator

Integrator is a term used in mathematics, engineering, and information technology to denote an entity that performs integration or unifies disparate components. The exact meaning depends on the context, but common threads include accumulation, combination, or unification.

In calculus, integration is the inverse operation of differentiation. The indefinite integral or antiderivative F of a function f satisfies F' = f, and the definite integral ∫[a,b] f(x) dx yields the net accumulation of quantities between a and b. Integrals are used to compute areas, total accumulated quantities, and physical quantities such as displacement when velocity is integrated over time. Numerical and symbolic methods exist to evaluate integrals.

In electrical engineering, an integrator is a circuit that outputs a signal proportional to the time integral of the input. An ideal integrator can be realized with an operational amplifier and a capacitor, giving a transfer function Vout(s) = Vin(s)/(sRC). Practical realizations include compensating components to limit drift, and leaky or finite-time-constant integrators to prevent saturation caused by offset voltages and noise.

In information technology and systems engineering, a systems integrator is a person or organization that builds a unified system by connecting hardware, software, and processes from multiple vendors. Responsibilities typically include requirements gathering, architectural design, interface specification, integration testing, deployment, and ongoing support.

Numerical integration is the computation of integrals using discrete methods. Common approaches include the trapezoidal rule, Simpson’s rule, and Gaussian quadrature, with variants that adaptively refine the approximation to control error.