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’
    • ‘He was integral to the whole process and I'll probably vote for him in the final round of voting.’
    • ‘He said: ‘This is integral to us bringing the jobs we have promised so of course we want to see it go ahead.’’
    • ‘Records are an integral requirement for organic certification.’
    • ‘Producer John Simon was an integral part of the Band's classic recordings.’
    • ‘The branches are not just appendages; they are integral to the whole.’
    • ‘In 1989 John Williamson asked Pixie to back him in his live shows, and for the next five years, Pixie became an integral part of John's live performances and recordings.’
    • ‘He says one of those ‘bite your thumb’ lines so integral to the whole adolescent love story.’
    • ‘Limousines, luxurious hotels, fancy restaurants and trips to the recording studio are all an integral part of a popstar's life.’
    • ‘They seem to be thrown in as an afterthought, rather than as an integral portion of the story.’
    • ‘An integral part of any call center is its recording system: it is used for training agents, ensuring quality across a campaign, legal compliance and more.’
    • ‘He has the speed, patience and quick burst necessary to make the cutback runs that are integral to the offense.’
    • ‘It is also rooted in a people's culture, and integral to their structure of thought.’
    • ‘Reputations aside, looking the part has certainly been integral to this almost episodic drama, at least as it's unfolded in the media.’
    • ‘Musically, it often has a really boring part but that part is integral to the chord structure.’
    • ‘A telecoms worker, for example, is both productive in providing a vital service and is also integral to the handling of information.’
    • ‘Since 1921 artistic, photographic and written records have formed an integral part of the Air Force's heritage.’
    • ‘Its core principle is that the teacher is integral not separate from his or her teaching, making the experience holistic.’
    • ‘‘I recognise that church and community halls are integral to community life and provide a social hub in a great many rural and urban areas,’ said Mr Howells.’
    • ‘Thus, they serve more as an accompaniment rather than an integral part of the book.’
    • ‘Logistic companies now form an integral part of the supply chain of any efficient business.’
    essential, fundamental, basic, intrinsic, inherent, constitutive, innate, structural
    View synonyms
    1. 1.1[attributive]Included as part of the whole rather than supplied separately.
      ‘the unit comes complete with integral pump and heater’
      • ‘This results in a heavier, stronger frame and also allows the use of an integral scope mounting system on the frame rather than the barrel.’
      • ‘Formerly a hotel, it has six en-suite bedrooms, four other bedrooms, an integral garage and, unusually, a recording studio.’
      • ‘Exclusive detailing includes integral roof rails, a rear screen that opens independently of the tailgate.’
      • ‘The integral power supply may be backed up by an external 24-volt DC supply, ensuring continuity of programming and easy mobile use.’
      • ‘Of the various firearms which include an integral lock, I know of none as neat and unobtrusive.’
      • ‘Included is an integral belt, skid-plate chest covering, face/rifle scope veil and elbow/knee pads.’
      • ‘Heat pump water heaters can be purchased as integral units with built in water storage tanks or as add-ons that can be retrofitted to an existing water heater tank.’
      • ‘The best option is either a pressurised system or a power shower, which is a mixer shower with an integral pump.’
      • ‘Scope rings to fit the integral receiver grooves are included with each T3.’
      • ‘Set over three floors, including an integral garage, this newly built three-bedroom house is in Kemp Town, close to all of Brighton's action.’
      • ‘The unit has an integral vacuum system that incorporates a turbomolecular pump as well as a backing scroll pump.’
      • ‘It also includes an integral altitude warning system to avoid deviations.’
      • ‘The same has been known to happen with the small keys that operate gun locks, whether they are separate or integral.’
      • ‘This then forms the cover, which includes both an integral hinge and a tear seam.’
      • ‘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.’
      • ‘Outside, the property includes a double integral garage, a paddock, extensive lawns and a vegetable garden.’
      • ‘I have a humongous bay window of gigantic proportions and my new curtains, once made up, will have cost me the slim sum of only £20 which includes integral linings.’
      • ‘The barrel length is 19.8 inches including the well-designed integral muzzle brake.’
      • ‘First, since they're luxury seats, they have a lot of integral features including power lumbar control, seatheaters, and side impact airbags.’
      • ‘As a result, many major manufacturers are equipping their firearms with integral locking devices or including trigger locks with every firearm.’
    2. 1.2[attributive]Having or containing all parts that are necessary to be complete.
      ‘the first integral recording of the ten Mahler symphonies’
      • ‘Now, of course, the composer appears on even major labels with some regularity, and there have been several integral recordings of the symphonies.’
  • 2Mathematics
    Of or denoted by an integer.

    • ‘Another analysis topic he studied was non-linear integral equations.’
    • ‘Under his guidance she worked on integral equations studying infinite dimensional linear spaces.’
    • ‘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.’
    1. 2.1Involving only integers, especially as coefficients of a function.
      • ‘He received his doctorate for a thesis entitled 'Contributions to the theory of integral functions of finite order' in 1929.’
      • ‘While he was doing this wide range of work he was also proving some of his deepest results in the study of integral functions.’
      • ‘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.’
      • ‘Some of them are about the theory of equations, others about integral functions.’

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.

    • ‘I remember feeling this way about derivatives (or was it integrals?).’
    • ‘It describes the integral of the area and the angular extents over which a radiation transfer problem is defined.’
    • ‘Hence an awareness of the inverse of differentiation began to evolve naturally and the idea that integral and derivative were inverses to each other were familiar to Barrow.’
    • ‘In Appendix B, the formula for calculating the integral of a logistic curve is given.’
    • ‘Both the peak values and the integrals under the characteristic fluorescence curves were measured.’
    1. 1.1A function satisfying a given differential equation.
      • ‘He wrote on algebraic integrals of certain differential equations.’
      • ‘He showed how to find integrals of a general system of partial differential equations by using sequential complete systems instead of passing to Jacobian systems.’
      • ‘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.’
      • ‘An estimate of an integral of a function can be obtained with a Monte Carlo integration.’

Origin

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

Pronunciation:

integral

/inˈteɡrəl//ˈin(t)əɡrəl/