Definition of integral in English:

integral

adjective ˈɪntɪɡr(ə)lɪnˈtɛɡr(ə)lˈin(t)əɡrəl

1Necessary to make a whole complete; essential or fundamental.
必需的；必要的；基本的，基础的
games are an integral part of the school's curriculum
体育活动是学校课程的基本一环。
systematic training should be integral to library management
系统培训应成为图书馆管理的基础。
Example sentencesExamples
- He says one of those ‘bite your thumb’ lines so integral to the whole adolescent love story.
- It is also rooted in a people's culture, and integral to their structure of thought.
- 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.
- He has the speed, patience and quick burst necessary to make the cutback runs that are integral to the offense.
- A telecoms worker, for example, is both productive in providing a vital service and is also integral to the handling of information.
- ‘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.
- Its core principle is that the teacher is integral not separate from his or her teaching, making the experience holistic.
- Reputations aside, looking the part has certainly been integral to this almost episodic drama, at least as it's unfolded in the media.
- They seem to be thrown in as an afterthought, rather than as an integral portion of the story.
- Logistic companies now form an integral part of the supply chain of any efficient business.
- 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.
- Limousines, luxurious hotels, fancy restaurants and trips to the recording studio are all an integral part of a popstar's life.
- 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 was integral to the whole process and I'll probably vote for him in the final round of voting.
- Thus, they serve more as an accompaniment rather than an integral part of the book.
- Records are an integral requirement for organic certification.
- Musically, it often has a really boring part but that part is integral to the chord structure.
- Since 1921 artistic, photographic and written records have formed an integral part of the Air Force's heritage.
- He said: ‘This is integral to us bringing the jobs we have promised so of course we want to see it go ahead.’
Synonyms
essential, fundamental, basic, intrinsic, inherent, constitutive, innate, structural
vital, indispensable, necessary, requisite
1. 1.1 Included as part of a whole rather than supplied separately.
  作为组成部分的
  the unit comes complete with integral pump and heater
  此设备是完整的，包括其组成部分的泵及加热装置。
  Example sentencesExamples
  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.
  The best option is either a pressurised system or a power shower, which is a mixer shower with an integral pump.
  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.
  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.
  Outside, the property includes a double integral garage, a paddock, extensive lawns and a vegetable garden.
  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.
  Included is an integral belt, skid-plate chest covering, face/rifle scope veil and elbow/knee pads.
  Formerly a hotel, it has six en-suite bedrooms, four other bedrooms, an integral garage and, unusually, a recording studio.
  The same has been known to happen with the small keys that operate gun locks, whether they are separate or integral.
  The barrel length is 19.8 inches including the well-designed integral muzzle brake.
  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.
  Scope rings to fit the integral receiver grooves are included with each T3.
  Exclusive detailing includes integral roof rails, a rear screen that opens independently of the tailgate.
  This then forms the cover, which includes both an integral hinge and a tear seam.
  The unit has an integral vacuum system that incorporates a turbomolecular pump as well as a backing scroll pump.
  Of the various firearms which include an integral lock, I know of none as neat and unobtrusive.
  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.
  It also includes an integral altitude warning system to avoid deviations.
  Synonyms
  built-in, inbuilt, integrated, incorporated, fitted, component, constituent
  rare integrant
2. 1.2 Having all the parts that are necessary to be complete.
  完整的
  the first integral recording of the ten Mahler symphonies
  Example sentencesExamples
  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, organic, composite, combined, aggregate, undivided, overall, gross, entire, complete, whole, total, full, intact
2Mathematics
Of or denoted by an integer.
〔数〕整数的
Example sentencesExamples
- Other topics he worked on include algebraic geometry, number theory and integral equations.
- Under his guidance she worked on integral equations studying infinite dimensional linear spaces.
- Another analysis topic he studied was non-linear integral equations.
- He was particularly interested in the courses in complex variable, integral equations and differential equations.
- He developed the relation between the algebra of matrices and integral equations as well as studying boundary value problems.
1. 2.1 Involving only integers, especially as coefficients of a function.
  （尤指作为函数系数）仅含整数的
  Example sentencesExamples
  He received his doctorate for a thesis entitled 'Contributions to the theory of integral functions of finite order' in 1929.
  Some of them are about the theory of equations, others about integral functions.
  Barnes next turned his attention to the theory of integral functions, where, in a series of papers, he investigated their asymptotic structure.
  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.

noun ˈɪntɪɡr(ə)lˈin(t)əɡrəl

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.
〔数〕积分。参见DEFINITE INTEGRAL , INDEFINITE INTEGRAL
See also definite integral, indefinite integral
Example sentencesExamples
- 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.
- Both the peak values and the integrals under the characteristic fluorescence curves were measured.
- I remember feeling this way about derivatives (or was it integrals?).
- 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.
1. 1.1 A function satisfying a given differential equation.
  满足微分方程的函数
  Example sentencesExamples
  An estimate of an integral of a function can be obtained with a Monte Carlo integration.
  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 work on algebra was an extension of Abel's work on algebraic functions and their integrals.
  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.

Usage

There are two possible pronunciations for integral as an adjective: one with the stress on the in- and the other with the stress on the -teg-. In British English, the second pronunciation is sometimes frowned on, but both are acceptable as standard

Derivatives

integrality

noun ɪntɪˈɡraləti

Bede Griffiths observes that the Vedic understanding of the integrality of the three worlds - physical, psychological and spiritual - is a profoundly holistic vision.
Example sentencesExamples
- 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.
- It involves a whole way of living in which meditation, life, and activity are meant to blend into one harmonious integrality.

integrally

adverb ˈɪntɪɡrəliɪnˈtɛɡrəli

‘People want to find out as much information as possible and be integrally involved in the decision-making process,’ he said.
Example sentencesExamples
- He looks for the best vocals as those that work integrally to the song.
- In contrast, I had to pay my rent to him integrally by law.
- The supportive view has been founded on the pragmatic basis that Britain is integrally linked through imports and exports with the broader European economy.
- They can be fabricated with near-invisible seams, and some brands offer a range of sinks and lavatories which can be fabricated integrally with the tops.

Origin

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

Definition of integral in US English:

integral

adjectiveˈin(t)əɡrəl

1Necessary to make a whole complete; essential or fundamental.
必需的；必要的；基本的，基础的
games are an integral part of the school's curriculum
体育活动是学校课程的基本一环。
systematic training should be integral to library management
系统培训应成为图书馆管理的基础。
Example sentencesExamples
- The branches are not just appendages; they are integral to the whole.
- Logistic companies now form an integral part of the supply chain of any efficient business.
- 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 says one of those ‘bite your thumb’ lines so integral to the whole adolescent love story.
- He said: ‘This is integral to us bringing the jobs we have promised so of course we want to see it go ahead.’
- Musically, it often has a really boring part but that part is integral to the chord structure.
- It is also rooted in a people's culture, and integral to their structure of thought.
- Limousines, luxurious hotels, fancy restaurants and trips to the recording studio are all an integral part of a popstar's life.
- He has the speed, patience and quick burst necessary to make the cutback runs that are integral to the offense.
- Producer John Simon was an integral part of the Band's classic recordings.
- Records are an integral requirement for organic certification.
- Reputations aside, looking the part has certainly been integral to this almost episodic drama, at least as it's unfolded in the media.
- He was integral to the whole process and I'll probably vote for him in the final round of voting.
- Since 1921 artistic, photographic and written records have formed an integral part of the Air Force's heritage.
- A telecoms worker, for example, is both productive in providing a vital service and is also integral to the handling of information.
- 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.
- They seem to be thrown in as an afterthought, rather than as an integral portion of the story.
- 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.
- Thus, they serve more as an accompaniment rather than an integral part of the book.
Synonyms
essential, fundamental, basic, intrinsic, inherent, constitutive, innate, structural
1. 1.1attributive Included as part of a whole rather than supplied separately.
  作为组成部分的
  the unit comes complete with integral pump and heater
  此设备是完整的，包括其组成部分的泵及加热装置。
  Example sentencesExamples
  Outside, the property includes a double integral garage, a paddock, extensive lawns and a vegetable garden.
  As a result, many major manufacturers are equipping their firearms with integral locking devices or including trigger locks with every firearm.
  The best option is either a pressurised system or a power shower, which is a mixer shower with an integral 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.
  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.
  Scope rings to fit the integral receiver grooves are included with each T3.
  This then forms the cover, which includes both an integral hinge and a tear seam.
  The barrel length is 19.8 inches including the well-designed integral muzzle brake.
  The integral power supply may be backed up by an external 24-volt DC supply, ensuring continuity of programming and easy mobile use.
  Included is an integral belt, skid-plate chest covering, face/rifle scope veil and elbow/knee pads.
  Of the various firearms which include an integral lock, I know of none as neat and unobtrusive.
  The unit has an integral vacuum system that incorporates a turbomolecular pump as well as a backing scroll pump.
  Exclusive detailing includes integral roof rails, a rear screen that opens independently of the tailgate.
  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.
  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.
  First, since they're luxury seats, they have a lot of integral features including power lumbar control, seatheaters, and side impact airbags.
  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.
  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.
  Synonyms
  built-in, inbuilt, integrated, incorporated, fitted, component, constituent
2. 1.2attributive Having or containing all parts that are necessary to be complete.
  完整的
  the first integral recording of the ten Mahler symphonies
  Example sentencesExamples
  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, organic, composite, combined, aggregate, undivided, overall, gross, entire, complete, whole, total, full, intact
2Mathematics
Of or denoted by an integer.
〔数〕整数的
Example sentencesExamples
- He was particularly interested in the courses in complex variable, integral equations and differential equations.
- Another analysis topic he studied was non-linear integral equations.
- Other topics he worked on include algebraic geometry, number theory and integral equations.
- Under his guidance she worked on integral equations studying infinite dimensional linear spaces.
- He developed the relation between the algebra of matrices and integral equations as well as studying boundary value problems.
1. 2.1 Involving only integers, especially as coefficients of a function.
  （尤指作为函数系数）仅含整数的
  Example sentencesExamples
  He received his doctorate for a thesis entitled 'Contributions to the theory of integral functions of finite order' in 1929.
  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.
  While he was doing this wide range of work he was also proving some of his deepest results in the study of integral functions.

nounˈin(t)əɡrəl

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.
〔数〕积分。参见DEFINITE INTEGRAL , INDEFINITE INTEGRAL
See also definite integral, indefinite integral
Example sentencesExamples
- 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.
- Both the peak values and the integrals under the characteristic fluorescence curves were measured.
- In Appendix B, the formula for calculating the integral of a logistic curve is given.
1. 1.1 A function satisfying a given differential equation.
  满足微分方程的函数
  Example sentencesExamples
  His first mathematical research was on analysis, in particular concentrating on integrals and solutions of differential equations.
  He wrote on algebraic integrals of certain differential equations.
  His work on algebra was an extension of Abel's work on algebraic functions and their integrals.
  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.
  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.

单词	integral
释义	Definition of integral in English: integral adjective ˈɪntɪɡr(ə)lɪnˈtɛɡr(ə)lˈin(t)əɡrəl 1Necessary to make a whole complete; essential or fundamental. 必需的；必要的；基本的，基础的 games are an integral part of the school's curriculum 体育活动是学校课程的基本一环。 systematic training should be integral to library management 系统培训应成为图书馆管理的基础。 Example sentencesExamples He says one of those ‘bite your thumb’ lines so integral to the whole adolescent love story. It is also rooted in a people's culture, and integral to their structure of thought. 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. He has the speed, patience and quick burst necessary to make the cutback runs that are integral to the offense. A telecoms worker, for example, is both productive in providing a vital service and is also integral to the handling of information. ‘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. Its core principle is that the teacher is integral not separate from his or her teaching, making the experience holistic. Reputations aside, looking the part has certainly been integral to this almost episodic drama, at least as it's unfolded in the media. They seem to be thrown in as an afterthought, rather than as an integral portion of the story. Logistic companies now form an integral part of the supply chain of any efficient business. 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. Limousines, luxurious hotels, fancy restaurants and trips to the recording studio are all an integral part of a popstar's life. 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 was integral to the whole process and I'll probably vote for him in the final round of voting. Thus, they serve more as an accompaniment rather than an integral part of the book. Records are an integral requirement for organic certification. Musically, it often has a really boring part but that part is integral to the chord structure. Since 1921 artistic, photographic and written records have formed an integral part of the Air Force's heritage. He said: ‘This is integral to us bringing the jobs we have promised so of course we want to see it go ahead.’ Synonyms essential, fundamental, basic, intrinsic, inherent, constitutive, innate, structural vital, indispensable, necessary, requisite 1.1 Included as part of a whole rather than supplied separately. 作为组成部分的 the unit comes complete with integral pump and heater 此设备是完整的，包括其组成部分的泵及加热装置。 Example sentencesExamples 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. The best option is either a pressurised system or a power shower, which is a mixer shower with an integral pump. 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. 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. Outside, the property includes a double integral garage, a paddock, extensive lawns and a vegetable garden. 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. Included is an integral belt, skid-plate chest covering, face/rifle scope veil and elbow/knee pads. Formerly a hotel, it has six en-suite bedrooms, four other bedrooms, an integral garage and, unusually, a recording studio. The same has been known to happen with the small keys that operate gun locks, whether they are separate or integral. The barrel length is 19.8 inches including the well-designed integral muzzle brake. 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. Scope rings to fit the integral receiver grooves are included with each T3. Exclusive detailing includes integral roof rails, a rear screen that opens independently of the tailgate. This then forms the cover, which includes both an integral hinge and a tear seam. The unit has an integral vacuum system that incorporates a turbomolecular pump as well as a backing scroll pump. Of the various firearms which include an integral lock, I know of none as neat and unobtrusive. 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. It also includes an integral altitude warning system to avoid deviations. Synonyms built-in, inbuilt, integrated, incorporated, fitted, component, constituent rare integrant 1.2 Having all the parts that are necessary to be complete. 完整的 the first integral recording of the ten Mahler symphonies Example sentencesExamples 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, organic, composite, combined, aggregate, undivided, overall, gross, entire, complete, whole, total, full, intact 2Mathematics Of or denoted by an integer. 〔数〕整数的 Example sentencesExamples Other topics he worked on include algebraic geometry, number theory and integral equations. Under his guidance she worked on integral equations studying infinite dimensional linear spaces. Another analysis topic he studied was non-linear integral equations. He was particularly interested in the courses in complex variable, integral equations and differential equations. He developed the relation between the algebra of matrices and integral equations as well as studying boundary value problems. 2.1 Involving only integers, especially as coefficients of a function. （尤指作为函数系数）仅含整数的 Example sentencesExamples He received his doctorate for a thesis entitled 'Contributions to the theory of integral functions of finite order' in 1929. Some of them are about the theory of equations, others about integral functions. Barnes next turned his attention to the theory of integral functions, where, in a series of papers, he investigated their asymptotic structure. 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. noun ˈɪntɪɡr(ə)lˈin(t)əɡrəl 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. 〔数〕积分。参见DEFINITE INTEGRAL , INDEFINITE INTEGRAL See also definite integral, indefinite integral Example sentencesExamples 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. Both the peak values and the integrals under the characteristic fluorescence curves were measured. I remember feeling this way about derivatives (or was it integrals?). 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. 1.1 A function satisfying a given differential equation. 满足微分方程的函数 Example sentencesExamples An estimate of an integral of a function can be obtained with a Monte Carlo integration. 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 work on algebra was an extension of Abel's work on algebraic functions and their integrals. 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. Usage There are two possible pronunciations for integral as an adjective: one with the stress on the in- and the other with the stress on the -teg-. In British English, the second pronunciation is sometimes frowned on, but both are acceptable as standard Derivatives integrality noun ɪntɪˈɡraləti Bede Griffiths observes that the Vedic understanding of the integrality of the three worlds - physical, psychological and spiritual - is a profoundly holistic vision. Example sentencesExamples 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. It involves a whole way of living in which meditation, life, and activity are meant to blend into one harmonious integrality. integrally adverb ˈɪntɪɡrəliɪnˈtɛɡrəli ‘People want to find out as much information as possible and be integrally involved in the decision-making process,’ he said. Example sentencesExamples He looks for the best vocals as those that work integrally to the song. In contrast, I had to pay my rent to him integrally by law. The supportive view has been founded on the pragmatic basis that Britain is integrally linked through imports and exports with the broader European economy. They can be fabricated with near-invisible seams, and some brands offer a range of sinks and lavatories which can be fabricated integrally with the tops. Origin Mid 16th century: from late Latin integralis, from integer 'whole' (see integer). Compare with integrate and integrity. Definition of integral in US English: integral adjectiveˈin(t)əɡrəl 1Necessary to make a whole complete; essential or fundamental. 必需的；必要的；基本的，基础的 games are an integral part of the school's curriculum 体育活动是学校课程的基本一环。 systematic training should be integral to library management 系统培训应成为图书馆管理的基础。 Example sentencesExamples The branches are not just appendages; they are integral to the whole. Logistic companies now form an integral part of the supply chain of any efficient business. 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 says one of those ‘bite your thumb’ lines so integral to the whole adolescent love story. He said: ‘This is integral to us bringing the jobs we have promised so of course we want to see it go ahead.’ Musically, it often has a really boring part but that part is integral to the chord structure. It is also rooted in a people's culture, and integral to their structure of thought. Limousines, luxurious hotels, fancy restaurants and trips to the recording studio are all an integral part of a popstar's life. He has the speed, patience and quick burst necessary to make the cutback runs that are integral to the offense. Producer John Simon was an integral part of the Band's classic recordings. Records are an integral requirement for organic certification. Reputations aside, looking the part has certainly been integral to this almost episodic drama, at least as it's unfolded in the media. He was integral to the whole process and I'll probably vote for him in the final round of voting. Since 1921 artistic, photographic and written records have formed an integral part of the Air Force's heritage. A telecoms worker, for example, is both productive in providing a vital service and is also integral to the handling of information. 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. They seem to be thrown in as an afterthought, rather than as an integral portion of the story. 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. Thus, they serve more as an accompaniment rather than an integral part of the book. Synonyms essential, fundamental, basic, intrinsic, inherent, constitutive, innate, structural 1.1attributive Included as part of a whole rather than supplied separately. 作为组成部分的 the unit comes complete with integral pump and heater 此设备是完整的，包括其组成部分的泵及加热装置。 Example sentencesExamples Outside, the property includes a double integral garage, a paddock, extensive lawns and a vegetable garden. As a result, many major manufacturers are equipping their firearms with integral locking devices or including trigger locks with every firearm. The best option is either a pressurised system or a power shower, which is a mixer shower with an integral 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. 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. Scope rings to fit the integral receiver grooves are included with each T3. This then forms the cover, which includes both an integral hinge and a tear seam. The barrel length is 19.8 inches including the well-designed integral muzzle brake. The integral power supply may be backed up by an external 24-volt DC supply, ensuring continuity of programming and easy mobile use. Included is an integral belt, skid-plate chest covering, face/rifle scope veil and elbow/knee pads. Of the various firearms which include an integral lock, I know of none as neat and unobtrusive. The unit has an integral vacuum system that incorporates a turbomolecular pump as well as a backing scroll pump. Exclusive detailing includes integral roof rails, a rear screen that opens independently of the tailgate. 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. 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. First, since they're luxury seats, they have a lot of integral features including power lumbar control, seatheaters, and side impact airbags. 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. 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. Synonyms built-in, inbuilt, integrated, incorporated, fitted, component, constituent 1.2attributive Having or containing all parts that are necessary to be complete. 完整的 the first integral recording of the ten Mahler symphonies Example sentencesExamples 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, organic, composite, combined, aggregate, undivided, overall, gross, entire, complete, whole, total, full, intact 2Mathematics Of or denoted by an integer. 〔数〕整数的 Example sentencesExamples He was particularly interested in the courses in complex variable, integral equations and differential equations. Another analysis topic he studied was non-linear integral equations. Other topics he worked on include algebraic geometry, number theory and integral equations. Under his guidance she worked on integral equations studying infinite dimensional linear spaces. He developed the relation between the algebra of matrices and integral equations as well as studying boundary value problems. 2.1 Involving only integers, especially as coefficients of a function. （尤指作为函数系数）仅含整数的 Example sentencesExamples He received his doctorate for a thesis entitled 'Contributions to the theory of integral functions of finite order' in 1929. 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. While he was doing this wide range of work he was also proving some of his deepest results in the study of integral functions. nounˈin(t)əɡrəl 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. 〔数〕积分。参见DEFINITE INTEGRAL , INDEFINITE INTEGRAL See also definite integral, indefinite integral Example sentencesExamples 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. Both the peak values and the integrals under the characteristic fluorescence curves were measured. In Appendix B, the formula for calculating the integral of a logistic curve is given. 1.1 A function satisfying a given differential equation. 满足微分方程的函数 Example sentencesExamples His first mathematical research was on analysis, in particular concentrating on integrals and solutions of differential equations. He wrote on algebraic integrals of certain differential equations. His work on algebra was an extension of Abel's work on algebraic functions and their integrals. 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. 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.
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