integral

Meanings

Plural: integrals

Noun

• the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
• 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.
• 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.
• Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
• 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.
• 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;
• 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.

Adjective Satellite

• existing as an essential constituent or characteristic
• constituting the undiminished entirety; lacking nothing essential especially not damaged; - Bacon
  • "a local motion keepeth bodies integral"

Adjective

• of or denoted by an integer

Adj

• Constituting a whole together with other parts or factors; not omittable or removable
• Of, pertaining to, or being an integer.
• Relating to integration (“the process of finding the integral [noun] of a function”).
• Being the root of some monic polynomial in A.
• Whole; undamaged.

Synonyms

antiderivative, built-in, constitutional, entire, essential, immanent, inbuilt, indefinite integral, infused, ingrained, inherent, instilled, intact, integral, intrinsic, inwrought, mul:∫, necessary, radical

Antonyms

derivative

Related Words

integer, integrity, integrous

Anagrams of integral