Definition of integral in English:
integral
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.
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 24volt 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.
builtin, 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.
2 Mathematics Of or denoted by an integer.
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.
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 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.
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.
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.
Derivatives

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