integral (redirected from integrality)

integral

Fundamental concept of calculus related to areas and other quantities modeled by functions. A definite integral gives the area between the graph of a function and the horizontal axis between vertical lines at the endpoints of an interval. It also calculates the net change in a system over an interval, thus leading to formulas for the work done by a varying force or the distance traveled by an object moving at varying speeds. When only the function is given, with no interval, it is known as an indefinite integral. The process of solving either a definite or an indefinite integral is called integration. According to the fundamental theorem of calculus, a definite integral can be calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). Integrals extend to higher dimensions through multiple integrals. See also line integral; surface integral.

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integral

1. Maths

a. of or involving an integral

b. involving or being an integer

2. Maths the limit of an increasingly large number of increasingly smaller quantities, related to the function that is being integrated (the integrand). The independent variables may be confined within certain limits (definite integral) or in the absence of limits (indefinite integral).

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integral [′int·ə·grəl]

(mathematics)

A solution of a differential equation is sometimes called an integral of the equation.

An elementaof a ringBis said to be integral over a ringAcontained inBif it is the root of a polynomial with coefficients inAand with leading coefficient 1.

definite Riemann integral indefinite integral