What does "integral" mean?

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.

What is a synonym for "integral"?

Common synonyms include: intact, a certain, aggregate, algorismic, algorithmic, aliquot.

How do you pronounce "integral"?

Pronounced //ˈɪntəɡɹəl//.

Integral

//ˈɪntəɡɹəl// adj, name, noun

adj, name, noun ·Common ·High school level

Definitions

Noun

1
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 integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!"
2
the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x) wordnet
3
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. specifically
4
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.
"The integral of #92;frac#123;1#125;#123;x#125; on #91;#92;frac#123;1#125;#123;2#125;,1#93; is #92;ln(2), but the integral of the same function on (0,1#93; diverges. In notation, #92;int#95;#92;frac#123;1#125;#123;2#125;¹#92;frac#123;1#125;#123;x#125;dx#61;#92;ln(2), but #92;int#95;0¹#92;frac#123;1#125;#123;x#125;dx#61;#92;infty."
5
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 integral of x² is #92;frac#123;x³#125;#123;3#125; plus a constant."

Show 1 more definition

6
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. historical, obsolete

Adjective

1
Constituting a whole together with other parts or factors; not omittable or removable.
"Ceasing to do evil, and doing good, are the two great integral parts that complete this duty."
2
Of, pertaining to, or being an integer.
3
Relating to integration (“the process of finding the integral [noun] of a function”).
4
Being the root of some monic polynomial in A.
5
Whole; undamaged. obsolete
"A local motion keepeth bodies integral."

Adjective

1
constituting the undiminished entirety; lacking nothing essential especially not damaged wordnet
2
existing as an essential constituent or characteristic wordnet
3
of or denoted by an integer wordnet