Integration vs. Integral — What's the Difference?

The process of summing parts to find a whole.

A mathematical expression representing the accumulation of quantities.

The process of accumulating changes to find a total effect.

A tool for calculating areas, volumes, and total quantities.

The act of calculating the area under a curve of a function across an interval.

Constituting the undiminished entirety; lacking nothing essential especially not damaged;

The application of integrating techniques to solve differential equations.

The result of integrating a function.

A method in calculus for finding antiderivatives.

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

The act or process of integrating.

Necessary to make a whole complete; essential or fundamental

The state of becoming integrated.

Of or denoted by an integer.

The bringing of people of different racial or ethnic groups into unrestricted and equal association, as in society or an organization; desegregation.

A function of which a given function is the derivative, i.e. which yields that function when differentiated, and which may express the area under the curve of a graph of the function.

(Psychology) The organization of the psychological or social traits and tendencies of a personality into a harmonious whole.

Essential or necessary for completeness; constituent

(Mathematics) The process of computing an integral; the inverse of differentiation.

Possessing everything essential; entire.

(Electronics) The process of placing more than one integrated circuit on a single microchip.

Expressed or expressible as or in terms of integers.

The act or process of making whole or entire.

Expressed as or involving integrals.

The process of combining with compatible elements in order to incorporate them.

A complete unit; a whole.

(society) The process of fitting into a community, notably applied to minorities.

A number computed by a limiting process in which the domain of a function, often an interval or planar region, is divided into arbitrarily small units, the value of the function at a point in each unit is multiplied by the linear or areal measurement of that unit, and all such products are summed.

(US) racial integration.

A definite integral.

(calculus) The operation of finding the integral of a function.

An indefinite integral.

(biology) In evolution, the process by which the manifold is compacted into the relatively simple and permanent; supposed to alternate with differentiation as an agent in species' development.

Constituting a whole together with other parts or factors; not omittable or removable

The act or process of making whole or entire.

(mathematics) Of, pertaining to, or being an integer.

The operation of finding the primitive function which has a given function for its differential coefficient. See Integral.

(mathematics) Relating to integration.

In the theory of evolution: The process by which the manifold is compacted into the relatively simple and permanent. It is supposed to alternate with differentiation as an agent in development.

(obsolete) Whole; undamaged.

The action of incorporating a racial or religious group into a community

(mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.

The act of combining into an integral whole;

(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.

An operation used in the calculus whereby the integral of a function is determined

(mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.

(mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;

The fluent of a given fluxion in Newtonian calculus.

Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.

Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.

Of, pertaining to, or being, a whole number or undivided quantity; not fractional.

A whole; an entire thing; a whole number; an individual.

An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.

The result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)

Existing as an essential constituent or characteristic;

There are indefinite integrals (without limits) and definite integrals (with limits).

Integration is crucial for solving problems involving areas, volumes, and other quantities that accumulate over an interval.

Common techniques include substitution, partial fractions, and integration by parts.

Integration is used in fields like engineering to model continuous systems and processes.

Integral formulas provide direct methods for finding integrals of basic functions, facilitating efficient problem-solving.

An integral represents the accumulation of quantities, such as area, volume, or a total quantity.

Integration is the process of finding the integral of a function, often used to calculate areas under curves.

Integration is used to calculate quantities like displacement by integrating a velocity function over time.

Integration techniques are essential for simplifying and solving complex integrals, crucial in various applications of calculus.

Integration is the process, while the integral is the result of this process.

The constant of integration represents an infinite number of possible antiderivatives, reflecting the general solution to an integral.

Calculating the work done by a force over a distance is a practical application of an integral.

Indefinite integrals represent a family of functions and include a constant of integration, whereas definite integrals have specific limits and calculate a numerical value.

The area under a curve represents the integral of a function, important for calculating total quantities.

Definite integrals are represented by numerical values, whereas indefinite integrals are expressed as functions plus a constant.