integral
Part of speech: adj
noun
Morphological type: simple
Topics: algebra
mathematics
sciences
Etymology: Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.
Inflected forms:
form: more integral
pos: adj
tags: comparative
form: most integral
pos: adj
tags: superlative
form: integrals
pos: noun
tags: plural
Senses:
gloss: Constituting a whole together with other parts or factors; not omittable or removable.
pos: adj
examples: Ceasing to do evil, and doing good, are the two great integral parts that complete this duty.
When the verdict comes down, the transformation of the wunderkind founder of Theranos from black-clad genius to besuited milquetoast will be an integral part of the story.
gloss: Of, pertaining to, or being an integer.
pos: adj
gloss: Relating to integration (“the process of finding the integral [noun] of a function”).
pos: adj
gloss: Being the root of some monic polynomial in A.
pos: adj
gloss: Whole; undamaged.
pos: adj
tags: obsolete
examples: A local motion keepeth bodies integral.
gloss: 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.
pos: noun
examples: The integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!
gloss: 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.
pos: noun
tags: specifically
gloss: 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.
pos: noun
examples: 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.
Stokes' theorem relates the integral over a surface of the curl of a vector field to a line integral around the boundary of that surface: #92;int#95;S#92;nabla#92;times#92;mathbf#123;F#125;#92;cdotd#92;mathbf#123;S#125;#61;#92;int#95;#123;#92;partialS#125;#92;mathbf#123;F#125;#92;cdotd#92;mathbf#123;r#125;,.
gloss: 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;
pos: noun
examples: The integral of x² is #92;frac#123;x³#125;#123;3#125; plus a constant.
gloss: 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;
pos: noun
tags: historical
obsolete
Related words: integer
integrity
integrous
integrate
Derived words: differintegral
integral brick
integral closure
integral cosmology
integral cuboid
integral current
integral curvature
integral curve
integral domain
integral drawing
integral ecology
integral element
integral energy
integral extension
integral fast reactor
integral field unit
integral function
integral geometry
integral graph
integral homology group
integralism
integralist
integrality
integral kernel
integrally
integral membrane protein
integralness
integral number
integral politics
integral polygedron
integral polynomial
integral post-metaphysics
integral psychology
integral transformative practice
integral yoga
integraph
integrity
nonintegral
semi-integral
unintegral
Barnes integral
Choquet integral
contour integral
definite integral
double integral
flux integral
half-integral
Hellinger integral
improper integral
indefinite integral
integral calculus
integral equation
integral theory
integral transform
integration
iterated integral
Jackson integral
Lebesgue integral
line integral
logarithmic integral
Mellin-Barnes integral
ordered integral domain
particular integral
path integral formalism
Riemann integral
Riemann-Stieltjes integral
Sugeno integral
surface integral
triple integral
Volterra integral equation
volume integral
Translations:
lang: Arabic
word: تَكَامُل
roman: takāmul
lang: Armenian
word: ինտեգրալ
roman: integral
lang: Belarusian
word: інтэгра́л
roman: intehrál
lang: Bulgarian
word: интегра́л
roman: integrál
lang: Catalan
word: integració
lang: Chinese Cantonese
word: 積分 /积分
roman: zik¹ fan¹
lang: Hakka Chinese
word: chit-fûn-ho̍k
lang: Chinese Mandarin
word: 積分 /积分
roman: jī fēn
lang: Czech
word: integrál
lang: Dutch
word: integraal
lang: Esperanto
word: integralo
lang: Esperanto
word: integro
lang: Finnish
word: integraali
lang: French
word: intégrale
lang: Galician
word: integral
lang: Georgian
word: ინტეგრალი
roman: inṭegrali
lang: German
word: Integral
lang: Greek
word: ολοκλήρωμα
roman: oloklíroma
lang: Hebrew
word: אִינְטֶגְרָל
roman: integrál
lang: Hebrew
word: אַסְכֶּמֶת
roman: askémet
lang: Hungarian
word: integrál
lang: Icelandic
word: heildun
lang: Icelandic
word: tegrun
lang: Italian
word: integrale
lang: Japanese
word: 積分
roman: sekibun
lang: Kazakh
word: интеграл
roman: integral
lang: Khmer
word: អាំងតេក្រាល
roman: ʼangteekraal
lang: Korean
word: 적분
roman: jeokbun
lang: Kyrgyz
word: интеграл
roman: integral
lang: Malay
word: kamiran
lang: Manx
word: co-hym
lang: Mongolian
word: интеграл
roman: integral
lang: Norwegian
word: integral
lang: Polish
word: całka
lang: Polish
word: całka oznaczona
lang: Portuguese
word: integral
lang: Romanian
word: integrală
lang: Russian
word: интегра́л
roman: intɛgrál
lang: Serbo-Croatian
word: интѐгра̄л
lang: Serbo-Croatian
word: intègrāl
lang: Spanish
word: integral
lang: Sundanese
word: integral
lang: Swedish
word: integral
lang: Tagalog
word: lagom
lang: Thai
word: ปริพันธ์
roman: bpà-rí-pan
lang: Turkish
word: integral
lang: Ukrainian
word: інтегра́л
roman: intehrál
lang: Vietnamese
word: tích phân