integral
gb/ɪntˈɛɡɹəl/ us/ɪntˈɛɡɹəl/
B2
Anh
~ 6800
Các nghĩa
0 nghĩa
adjective
B2
property
1
essential and necessary part
Very important and needed so that something is complete or works well.
Mẫu sử dụng:
[something] is integral to [something]
Lỗi thường gặp:
Learners sometimes say *"integral for"* when they mean *"integral to"*. Use *integral to* when you say what thing needs it: "Sleep is integral to good health." Another mistake is using *integral* when they only mean *important*; *integral* usually means something is needed for completeness or proper function, not just helpful.
Từ đồng nghĩa
essential (Stronger and more direct about something being absolutely needed; very close in meaning and register.)
|
fundamental (Suggests forming a basic foundation or base, often in more formal or abstract contexts.)
|
vital (Adds a sense of great importance, sometimes with an emotional or urgent tone.)
Từ trái nghĩa
nonessential (States directly that something is not necessary or required.)
|
minor (Suggests something is less important or has little influence on the whole.)
Cụm từ đi kèm
integral part of
|integral role
|integral component
|integral to the success
|integral member
|integral to the system
Chủ đề
daily_life
|work
|society
|core_vocabulary
Ví dụ
- Trust is integral to any healthy relationship.
- Local volunteers play an integral role in running the festival.
- Public transport is an integral part of life in big cities.
- Regular backups are integral to our data security plan.
- These community centers are integral to the city’s social support system.
Ví dụ cho người học
- Good communication is integral to a strong team.
- Exercise is integral to a healthy lifestyle.
- Reading is an integral part of my daily routine.
- Honesty is integral to their company culture.
- Clean water is integral to human life.
adjective
formal
C1
property
2
forming a whole, complete
Having all parts together so that something is whole and not divided.
Mẫu sử dụng:
[something] forms an integral whole
Lỗi thường gặp:
Learners may confuse this sense with the more common *"essential"* sense and use *integral* before a single item (e.g. *"an integral door"*). In this meaning, *integral* usually describes something abstract (a system, approach, vision, whole) rather than a simple physical object.
Từ đồng nghĩa
whole (More common and less formal; simply means not divided or broken.)
|
complete (Focuses on having all parts needed, without the formal or abstract tone of "integral".)
Từ trái nghĩa
fragmented (Highlights something being broken into pieces rather than forming one whole.)
|
partial (Emphasizes that only some parts are present, not the entire whole.)
Cụm từ đi kèm
integral whole
|integral system
|integral structure
|integral vision
|integral approach
Chủ đề
academic
|philosophy
|society
|core_vocabulary
Ví dụ
- The report presents an integral view of the region’s economic and social challenges.
- These policies must be seen as part of an integral system, not as separate measures.
- We need an integral approach that connects education, housing, and healthcare.
- The novel offers an integral portrait of life in a small coastal town.
- Urban planning should aim at creating an integral whole, not isolated projects.
Ví dụ cho người học
- The book gives an integral picture of life in the city.
- The plan is an integral whole and all parts work together.
- We must see the school as an integral system, not just separate classes.
- Her study offers an integral view of the problem.
- They want an integral solution, not many small answers.
adjective
technical
C1
property
3
relating to calculus integrals
Talking about or using integrals in calculus.
Mẫu sử dụng:
integral [noun]
Lỗi thường gặp:
Learners sometimes think *integral calculus* means "very important calculus" because of the everyday meaning of *integral*. In mathematics, this sense strictly refers to calculus based on integration, not importance.
Từ đồng nghĩa
integrational (A rare technical term; in practice, mathematicians simply use "integral" for things involving integrals.)
Từ trái nghĩa
differential (In calculus, describes things related to differentiation rather than integration, often contrasted with "integral" (e.g. differential vs. integral equations).)
Cụm từ đi kèm
integral calculus
|integral equation
|integral transform
|integral operator
|integral function
Chủ đề
mathematics
|science
|education
Ví dụ
- The course covers both differential and integral calculus.
- We will now study integral equations and their applications.
- This theorem plays a central role in integral geometry.
- The paper introduces a new integral operator on this function space.
- Integral transforms are powerful tools in mathematical physics.
Ví dụ cho người học
- Today we learned about integral calculus in class.
- This is an integral equation, not a simple algebra problem.
- The book has a chapter on integral methods.
- Integral operators are used in advanced mathematics.
- She is doing research on integral transforms.
Danh từ
technical
C1
entity
4
result of integration
In calculus, the answer you get when you integrate a function.
Mẫu sử dụng:
the integral of [function]
Lỗi thường gặp:
Learners often mix up *integral* and *integration*. *Integral* is the result (or expression) you get, while *integration* is the process. For example: "Find the integral of x" (result), not "Find the integration of x."
Từ đồng nghĩa
antiderivative (More precise for indefinite integrals; refers to a function whose derivative is the given function.)
|
primitive (Used mainly in some mathematical traditions (e.g. French) as a synonym for "antiderivative"; less common in general English usage.)
Từ trái nghĩa
derivative (In calculus, the basic complementary operation to integration; often conceptually paired with integral as an opposite process.)
Cụm từ đi kèm
definite integral
|indefinite integral
|compute the integral
|evaluate the integral
|integral sign
|integral of
Chủ đề
mathematics
|science
|education
Ví dụ
- The integral of x² is x³/3 + C.
- We can use substitution to evaluate this definite integral.
- This table lists common integrals you should memorize.
- The area under the curve is given by this integral.
- To solve the problem, first write down the integral and then choose an appropriate method.
Ví dụ cho người học
- We learned how to find the integral of simple functions.
- The teacher asked us to compute this definite integral.
- I still make mistakes when I evaluate integrals.
- This formula helps you find the integral faster.
- The integral gives the area under the graph.
adjective
technical
C2
property
5
consisting of whole numbers
In mathematics, made only of whole numbers, with no fractions or decimals.
Mẫu sử dụng:
integral [noun]
Lỗi thường gặp:
Learners may confuse *integral* with *integer* and use them in the wrong position. Use *integer* as a noun ("an integer"), and *integral* as an adjective before a noun ("an integral solution").
Từ đồng nghĩa
integer (Usually a noun; sometimes used attributively (e.g. "integer solution"), where *integral* is more traditional in some technical phrases.)
Từ trái nghĩa
fractional (Emphasizes the presence of a non‑whole, fractional part, opposite to an integral or whole-number value.)
|
real-valued (Can include non-integer values; used in contrast to "integral" when specifying what kind of values a solution or variable can take.)
Cụm từ đi kèm
integral solution
|integral domain
|integral matrix
|integral coefficients
|integral lattice
Chủ đề
mathematics
|science
|education
Ví dụ
- We are only interested in integral solutions to this equation.
- The algorithm searches for the smallest integral vector satisfying the constraints.
- This is an integral matrix, since all its entries are integers.
- In number theory, we often work within an integral domain.
- The model requires the decision variables to be integral, not continuous.
Ví dụ cho người học
- The teacher asked us to find an integral solution to the problem.
- All the values in this table are integral numbers.
- In this exercise, x must be integral, not a fraction.
- We need integral values for this variable.
- This method works only with integral data.
Ngữ pháp
Dạng từ điển
integral
IPA
GB/ɪntˈɛɡɹəl/
US/ɪntˈɛɡɹəl/
Âm tiết và trọng âm
in - teg - ral (3 âm tiết)
Stress on 2nd syllable (teg)
Các dạng từ
Adjective
- Base: integral
Noun
- Base: integral
- Plural: integrals
Họ từ
Forms
integrals
noun
Core family
Negative and opposite forms
disintegrate
verb
disintegration
noun
Advanced or less common
integrative
adjective
Cách diễn đạt
an integral part of
1/ən ɪntˈɛɡɹəl pˈɑɹt əv/
fixed phrase
a necessary part of something
A part that is needed so that something is complete or works well.
Ví dụ
- Teamwork is an integral part of our company culture.
- Freedom of the press is an integral part of a healthy democracy.
- Physical practice is an integral part of learning a musical instrument.
be integral in
1/bˈi ɪntˈɛɡɹəl ˈɪn/
fixed phrase
play an essential role in
To be very important in making something happen or in reaching a result.
Ví dụ
- She was integral in organizing the charity event.
- Community leaders were integral in bringing peace to the region.
- Technology has been integral in improving medical care.
be integral to
1/bˈi ɪntˈɛɡɹəl tə/
fixed phrase
be essential for something
To be very important and needed so that something is complete or works well.
Ví dụ
- Innovation is integral to the company’s long-term success.
- Listening is integral to good communication.
- These values are integral to our way of life.
form an integral part of
1/fˈɔɹm ən ɪntˈɛɡɹəl pˈɑɹt əv/
fixed phrase
formal
constitute an essential part
To be one of the important parts that together make a whole thing.
Ví dụ
- Local traditions form an integral part of the nation’s identity.
- Research and teaching form an integral part of the university’s mission.
- Public transport forms an integral part of the city’s infrastructure.