Definition of integral in English:

integral

Syllabification: in·te·gral
Pronunciation: /ˈin(t)əɡrəl
 
, inˈteɡrəl
 
/

adjective

1Necessary to make a whole complete; essential or fundamental: games are an integral part of the school’s curriculum systematic training should be integral to library management
More example sentences
  • He was integral to the whole process and I'll probably vote for him in the final round of voting.
  • Musically, it often has a really boring part but that part is integral to the chord structure.
  • He says one of those ‘bite your thumb’ lines so integral to the whole adolescent love story.
Synonyms
essential, fundamental, basic, intrinsic, inherent, constitutive, innate, structural; vital, necessary, requisite
1.1 [attributive] Included as part of the whole rather than supplied separately: the unit comes complete with integral pump and heater
More example sentences
  • The integral power supply may be backed up by an external 24-volt DC supply, ensuring continuity of programming and easy mobile use.
  • A future mission should treat a Mars lander as an integral part of the whole spacecraft rather than one of its instruments, the report said.
  • The best option is either a pressurised system or a power shower, which is a mixer shower with an integral pump.
Synonyms
built-in, integrated, incorporated, included
1.2 [attributive] Having or containing all parts that are necessary to be complete: the first integral recording of the ten Mahler symphonies
More example sentences
  • Now, of course, the composer appears on even major labels with some regularity, and there have been several integral recordings of the symphonies.
Synonyms
unified, integrated, comprehensive, composite, combined, aggregate; complete, whole
2 Mathematics Of or denoted by an integer.
More example sentences
  • Other topics he worked on include algebraic geometry, number theory and integral equations.
  • He developed the relation between the algebra of matrices and integral equations as well as studying boundary value problems.
  • He was particularly interested in the courses in complex variable, integral equations and differential equations.
2.1Involving only integers, especially as coefficients of a function.
More example sentences
  • To do this we make adjustments in the integral functions.
  • Barnes next turned his attention to the theory of integral functions, where, in a series of papers, he investigated their asymptotic structure.
  • He received his doctorate for a thesis entitled 'Contributions to the theory of integral functions of finite order' in 1929.

noun

Mathematics Back to top  
1A 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. See also definite integral, indefinite integral.
More example sentences
  • In Appendix B, the formula for calculating the integral of a logistic curve is given.
  • It describes the integral of the area and the angular extents over which a radiation transfer problem is defined.
  • Both the peak values and the integrals under the characteristic fluorescence curves were measured.
1.1A function satisfying a given differential equation.
More example sentences
  • He wrote on algebraic integrals of certain differential equations.
  • His first mathematical research was on analysis, in particular concentrating on integrals and solutions of differential equations.
  • His work on algebra was an extension of Abel's work on algebraic functions and their integrals.

Origin

mid 16th century: from late Latin integralis, from integer 'whole' (see integer). Compare with integrate and integrity.

Derivatives

integrality

Pronunciation: /ˌintiˈɡralitē/
noun
More example sentences
  • Bede Griffiths observes that the Vedic understanding of the integrality of the three worlds - physical, psychological and spiritual - is a profoundly holistic vision.
  • This missing part of a text, called the ‘intertext,’ put like a spell upon the reader, forces him to respond out of his very need for completion, integrality.
  • On the contrary, Sylvia Chen rejects her own perceptions as fragmented and objectified and instead discovers the integrality of the landscape to her self.

integrally

adverb
More example sentences
  • The supportive view has been founded on the pragmatic basis that Britain is integrally linked through imports and exports with the broader European economy.
  • In contrast, I had to pay my rent to him integrally by law.
  • He looks for the best vocals as those that work integrally to the song.

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