Inta

intA is a plain-text way of referring to the definite integral over a specified subset A of the domain, commonly written in mathematical notation as ∫_A f(x) dμ(x) or ∫_A f dμ. The symbol int stands for integration, and the subscript A designates the region or set over which the integration is performed. In practice, the exact meaning depends on the context and the underlying measure μ being used (for example, the Lebesgue measure on real numbers or the standard arclength or volume measures in geometry).

When A is a measurable subset of the domain and f is integrable with respect to μ, the integral ∫_A f represents the accumulation of f over A. In many standard contexts, this is equivalent to ∫ f dμ restricted to A, or to ∫ f(x) 1_A(x) dμ(x), where 1_A is the indicator function of A. The result can vary with the choice of measure and the notion of integrability (such as Riemann, Lebesgue, or improper integrals).

Common applications include probabilities, where P(A) = ∫_A p(x) dx for a density p, and physics or engineering, where quantities like mass or total energy are computed as ∫_A ρ(x) dV over a region A. The notation is also used in geometry and analysis to express integrals over regions, surfaces, or volumes, often extending to higher dimensions as ∫_A f dμ in R^n.

Related concepts include the indicator function, measure theory, Lebesgue and Riemann integrals, and theorems such as Fubini’s and the monotone convergence theorem, which provide ways to evaluate or relate integrals over sets.