# integral

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

## Definition of *integral* in English:

### 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

*Included as part of the whole rather than supplied separately:* [ attributive] *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.

**built-in**, integrated, incorporated, included

1.2

*Having or containing all parts that are necessary to be complete:* [ attributive] *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*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.

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.

### Origin

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

### Derivatives

- 1
#### integrality

- 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.

- 2
#### 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.

Pronunciation: /ˌintiˈɡralitē/

noun## Definition of **integral** in:

- British & World English dictionary
- English synonyms
- US English synonyms
- Spanish dictionary

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