Using the word integral - Word и Excel - помощь в работе с программами

Has anyone ever told you that you’re an integral part of a team, leaving you to wonder what the word integral even means? Not to worry; we’re here to help!

In this guide, we’re exploring the English word integral to uncover its definition, usage, synonyms, and more. So if you’ve ever been curious about the term integral — keep reading.

What Is the Definition of Integral?

/ɪnˈtɛg rəl/ /ɪnˈtɛgrəl/ /ˈɪn tɪ grəl/ /ˈɪntɪgrəl/

If we look at any of the many trusted English Language Dictionaries, we will see that integral means something that is very important and more often than not, necessary. A good example of this would be stating that you are an integral part of your team — the usage of integral here implies that your team would simply not function without you.

When used as an adjective, integral has a few slightly varying definitions, which we have listed for you to review below:

Composed of confident parts
Crucial to completeness
Lacking nothing essential

Additionally, the Collins Dictionary states that integral — when used in reference to mathematics — refers to either a definite integral or indefinite integral. Below you will find a quick guide on both definite and indefinite integrals:

Definite Integral — A definite integral or Riemann integral, of a function f(x), is an integral in which the range of integration is specified. A Riemann integral’s value equals the area on a graph bounded by two given coordinates, the x-axis and a curve.

Indefinite integral — also called an antiderivative of a function f(x); refers to any function that, when differentiated, yields a given function. Furthermore, integration is the process of finding an indefinite integral. It should be noted that an indefinite integral is most commonly seen in symbolic form, which is written ∫ f(x)dx where f(x) is the given function.

What Are the Synonyms and Antonyms of Integral?

Now that you have a better understanding of the word integral let’s take a look at some synonyms and antonyms!

Synonyms of integral include:

Essential
Key
Necessary
Major
Indispensable
Joined at the hip
Thick as thieves
In each other’s pocket
As one
Tied up
Must have
Inherent
Principal
Crucial
Fundamental
At the heart of
Complete
Entire
Thorough
Full-fledged
All-inclusive
Exhaustive
Total
Unified
Built-in
Incorporated
Accompanying
Constituent
Part and parcel
Intrinsic
Deep down
Bred in the bone
In your blood
Natural born
Deep-seated
All important
Pre-eminent
Meat and potatoes
Prerequisite
Vitally important
Called for
High priority
Primary
Obligatory

Antonyms of integral include:

Inessential
Unnecessary
To no purpose
De trop
Not required
Uncalled for
Too much
Replaceable
Groundless
Disposable
Gratuitous
Half-finished
Surplus
Fractional
Partially complete
Trivial
Skippable
Not concluded
Partial
Imperfect
Not finished
Fractional
Incomplete
Unfinished
Limited
Wide of the mark
Not pertinent
Off the point
Beside the point
Inexact
Part
Unwhole
Reduced
Supplemental
Contributory
Ancillary
Supporting
Adventitious
Of no account
Affected
Nurtured
Not included

How Can You Use Integral in a Sentence?

By now, you likely understand that integral simply means necessary to make a whole complete, but do you know how to use it in a sentence? Not to worry— integral can be a challenging term to fully grasp! That said, here are some example sentences for you to review:

“Did you know that the definition of integral is different when used in calculus?”

“Everyone knows that the engine is an integral part of just about any motor vehicle.”

“My manager told me that I was an integral part of the team, which is why I was given a raise.”

“Tammy occupied herself by inventing the differential and integral calculus.”

“Look, you’re an integral part of the group, so it would be a major loss for us if you left.”

“Marissa was especially interested in the courses in integral equations and differential equations.’

“Something that is considered an integral part of something is ultimately an essential part of that thing.”

“We learned that the fundamental theorem of calculus relates definite integrals with differentiation in class today.”

“You’re going to need to make adjustments in the integral functions if you want to do this.”

“Despite being an integral member of the New York book club, I decided it was time to leave.”

“Though she was only one person, Sarah was an integrap part of the resistance movement.”

“Protein and healthy fats are intregal to a well-balanced diet.”

“Bob is an integral team member due to his many years of experience in customer service.”

“Seeing as I am integral to our team hitting the monthly quota, I think it’s only fair that I get a raise.”

What Are Translations of Integral?

Want to learn how to say our word of the day in a different language? We’ve got you covered!

Translations of integral, which have been provided by the Cambridge American English Dictionary, include:

American English — integral
Italian — integrante
Afrikaans — Integrale
Polish — całka
Russian — интеграл
Japanese — 絶対必要な
Korean — 필수의
Arabic — متكاملة
European Portuguese — integral
Spanish — integrante
Ukrainian — Інтеграл
Thai — ที่จำเป็น
Greek — ακέραιος
Vietnamese — tích phân
British English — integral
Brazilian Portuguese — integral
Chinese — 构成整体所必需的
European Spanish — integrante
French — intégrant
German — wesentlich

Conclusion

So, what does our word of the day mean, you ask?

Simply put, integral means necessary to completeness. Something that is integral is very important. In other words, if you’re an integral part of the team, it means that the team can’t function properly without you.

When used in mathematics, however, the term integral has a slightly different meaning as it refers to a function or number that gives the area under a curve on a graph between two points.

Want to discover the meaning behind more complex words like integral? Check out our website today!

Sources:

INTEGRAL: definition | Cambridge English Dictionary

Integral definition and meaning | Collins English Dictionary

Integral Definition & Meaning | Dictionary.com

Kevin Miller is a growth marketer with an extensive background in Search Engine Optimization, paid acquisition and email marketing. He is also an online editor and writer based out of Los Angeles, CA. He studied at Georgetown University, worked at Google and became infatuated with English Grammar and for years has been diving into the language, demystifying the do’s and don’ts for all who share the same passion! He can be found online here.

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интегральный, неотъемлемый, встроенный, интеграл, целое число

прилагательное ↓

- неотъемлемый, существенный

an integral part of smth. — неотъемлемая часть чего-л.
to be integral to smth. — быть неотъемлемой частью /составлять неотъемлемую часть/ чего-л.

- редк. целый, полный, цельный

his integral works are lost — все его произведения утеряны

- мат. интегральный

integral calculus — интегральное исчисление

существительное

- нечто целое, неделимое
- мат. интеграл

Мои примеры

Словосочетания

to compute the value of an integral — вычислить интеграл
integral of — интеграл от
integral over — интеграл по
integral inequality — интегральное неравенство
complete integral — полный интеграл
strictly integral — строго целый
integral feature — неотъемлемое свойство
integral part — неотъемлемая часть
essential integral — существенный интеграл
logarithmic integral — интегральный логарифм

Примеры с переводом

Vegetables are an integral part of our diet.

Овощи являются неотъемлемой частью нашего рациона.

Freedom of speech is integral to democracy.

Свобода слова — неотъемлемая составляющая демократии.

She had become an integral part of their lives.

Она стала неотъемлемой частью их жизни.

Statistics are integral to medical research.

Статистические данные являются неотъемлемой частью медицинских исследований.

Common meals are an integral part of family life.

Совместные трапезы — неотъемлемая часть семейной жизни.

Practical work forms an integral part of the course.

Практическая работа является неотъемлемой частью этого курса.

They believe that their names and likenesses are integral parts of themselves.

Они думают, что их имена и их изображения — неотъемлемая часть их самих.

Patient confidentiality has long been an integral part of a physician’s professional devoir.

Соблюдение конфиденциальности в отношении пациента уже давно стало неотъемлемой частью профессионального долга врача.

Примеры, ожидающие перевода

…a car dealer respected for his integral honesty and straightforwardness with customers…

Для того чтобы добавить вариант перевода, кликните по иконке ☰, напротив примера.

Возможные однокоренные слова

integrality — целостность, полнота
integrally — целиком, полностью, в целом, интегрально, как целая часть

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How do you use the word integral?

Integral in a Sentence ?

The engine is an integral part of any motor vehicle.
Sometimes, even the smallest part in a car can be integral to the operation.
Protein is an integral part of any well-balanced diet.
Though he was only one man, he was an integral part of the resistance movement.

What does the word Intrical mean?

(Entry 1 of 2) 1a : essential to completeness : constituent an integral part of the curriculum. b(1) : being, containing, or relating to one or more mathematical integers. (2) : relating to or concerned with mathematical integration or the results of mathematical integration.

What is a integral person?

It is not primarily a set of character traits such as honesty, consistency, or morality. When someone becomes an ‘integral person’, their integrity has come about through a ‘learning process by which intellectual, moral and ethical standards are created. ‘ In Kolb’s view, the ‘pinnacle of development is integrity.

What is integral means in Tagalog?

integral; entire; intact. constituting the undiminished entirety; lacking nothing essential especially not damaged.

What is an integrant?

noun. an integrant part. a solid, rigid sheet of building material composed of several layers of the same or of different materials.

Is Important another word for Integral?

Integral Synonyms – WordHippo Thesaurus….What is another word for integral?

essential	key
indispensable	major
requisite	significant
vital	central
consequential	critical

What is the best synonyms for Integral?

other words for integral

elemental.
essential.
indispensable.
intrinsic.
component.
constituent.
fundamental.
requisite.

What is another word for host?

MC	emcee
presenter	anchor
announcer	anchorman
anchorwoman	compere
moderator	link person

What is another word for central idea?

Synonyms for central idea in English central thought; keynote; main idea; basic principle; central idea; basic thought.

What does the word central mean?

(Entry 1 of 2) 1 : containing or constituting a center. 2 : of primary importance : essential, principal the central character of the novel. 3a : situated at, in, or near the center the central part of the state.

What means almost the same as central?

Synonyms for central. centrist, middle-of-the-road, moderate.

How do you use the word Central?

Ventral sentence example

The right ventricle occupies the ventral portion of the heart.
The whole ventral surface of the pericardium is exposed when the sternum is removed.
It is protruded and retracted by special muscles which are partly attached to the ventral , distal end of the ilium.

What is another name for a central government?

Always equivalent in a federation is the federal government, which may have distinct powers at various levels authorized or delegated to it by its federated states, though the adjective ‘central’ is sometimes also used to describe it.

What do you call a person with principles?

A stickler is a person who insists on behaving a certain way (usually adherent to a fixed principle or set of principles). Definition: https://en.oxforddictionaries.com/definition/stickler. noun. A person who insists on a certain quality or type of behaviour. ‘he’s a stickler for accuracy’

What is a set of principles called?

doctrine. noun. a set of principles or beliefs, especially religious, political or legal ones.

What is a person of principle?

A person of principle means someone who faithfully follows their principle or set of principles rather than abandoning them when convenient. Such a person would live his or her life according to the moral guidelines set out in the Bible, especially for instance the Ten Commandments.

What is principle mean?

1 : a general or basic truth on which other truths or theories can be based scientific principles. 2 : a rule of conduct based on beliefs of what is right and wrong. 3 : a law or fact of nature which makes possible the working of a machine or device the principle of magnetism.

Is it good to have principles?

Principles allow you to live and work to your best while enabling others to understand the best way to interact with you. When you behave in a manner which is consistent with your principles, you feel confident and empowered. You know that you are being true to who you are.

What is your personal purpose?

A personal purpose statement defines who you are. It reflects your passions and values. It provides clarity as you set goals. Your sense of purpose steers how you want your story to go. A personal purpose statement simplifies your direction – your goals will either align with your definite major purpose or it doesn’t.

Источник

From Simple English Wikipedia, the free encyclopedia

Integration is about finding the surface s, given a, b and y = f(x). The formula for the integral from a to b, graphed above, is:
Formula: ${displaystyle int limits _{a}^{b}f(x),dx}$

What is the integral (animation)

In calculus, an integral is the space under a graph of an equation (sometimes said as «the area under a curve»). An integral is the reverse of a derivative, and integral calculus is the opposite of differential calculus. A derivative is the steepness (or «slope»), as the rate of change, of a curve. The word «integral» can also be used as an adjective meaning «related to integers».

The symbol for integration, in calculus, is: ${displaystyle textstyle int _{,}^{,}}$ as a tall letter «S».^[1]^[2]^[3]

Integrals and derivatives are part of a branch of mathematics called calculus. The link between these two is very important, and is called the fundamental theorem of calculus.^[4] The theorem says that an integral can be reversed by a derivative, similar to how an addition can be reversed by a subtraction.

Integration helps when trying to multiply units into a problem. For example, if a problem with rate, ${displaystyle left({tfrac {text{distance}}{text{time}}}right)}$ , needs an answer with just distance, one solution is to integrate with respect to time. This means multiplying in time to cancel the time in ${displaystyle left({tfrac {text{distance}}{text{time}}}right)times {text{time}}}$ . This is done by adding small slices of the rate graph together. The slices are close to zero in width, but adding them together indefinitely makes them add up to a whole. This is called a Riemann sum.

Adding these slices together gives the equation that the first equation is the derivative of. Integrals are like a way to add many tiny things together by hand. It is like summation, which is adding . The difference with integration is that we also have to add all the decimals and fractions in between.^[4]

Another time integration is helpful is when finding the volume of a solid. It can add two-dimensional (without width) slices of the solid together indefinitely—until there is a width. This means the object now has three dimensions: the original two and a width. This gives the volume of the three-dimensional object described.

Methods of Integration[change | change source]

Antiderivative[change | change source]

By the fundamental theorem of calculus, the integral is the antiderivative.

If we take the function , for example, and anti-differentiate it, we can say that an integral of is ${displaystyle x^{2}}$ . We say an integral, not the integral, because the antiderivative of a function is not unique. For example, ${displaystyle x^{2}+17}$ also differentiates to .
Because of this, when taking the antiderivative a constant C must be added. This is called an indefinite integral. This is because when finding the derivative of a function, constants equal 0, as in the function

${displaystyle f(x)=5x^{2}+9x+15,}$

. Note the 0: we cannot find it if we only have the derivative, so the integral is

${displaystyle int (10x+9),dx=5x^{2}+9x+C}$

Simple Equations[change | change source]

A simple equation, such as ${displaystyle y=x^{2}}$ , can be integrated with respect to x using the following technique. To integrate, you add 1 to the power x is raised to, and then divide x by the value of this new power. Therefore, integration of a normal equation follows this rule:
^[3] ${displaystyle int _{,}^{,}x^{n}dx={frac {x^{n+1}}{n+1}}+C}$

The at the end is what shows that we are integrating with respect to x, that is, as x changes. This can be seen to be the inverse of differentiation. However, there is a constant, C, added when integrating. This is called the constant of integration.^[1] This is required because differentiating an integer results in zero, therefore integrating zero (which can be put onto the end of any integrand) produces an integer, C. The value of this integer would be found by using given conditions.

Equations with more than one terms are simply integrated by integrating each individual term:

${displaystyle int _{,}^{,}x^{2}+3x-2dx=int _{,}^{,}x^{2}dx+int _{,}^{,}3xdx-int _{,}^{,}2dx={frac {x^{3}}{3}}+{frac {3x^{2}}{2}}-2x+C}$

Integration involving e and ln[change | change source]

There are certain rules for integrating using e and the natural logarithm. Most importantly, ${displaystyle e^{x}}$ is the integral of itself (with the addition of a constant of integration):
^[3] ${displaystyle int _{,}^{,}e^{x}dx=e^{x}+C}$

The natural logarithm, ln, is useful when integrating equations with . These cannot be integrated using the formula above (add one to the power, divide by the power), because adding one to the power produces 0, and a division by 0 is not possible. Instead, the integral of is :
${displaystyle textstyle int _{,}^{,}{frac {1}{x}}dx=ln x+C}$ ^[3]

In a more general form:
${displaystyle int _{,}^{,}{frac {f'(x)}{f(x)}}dx=ln {|f(x)|}+C}$

The two vertical bars indicated a absolute value; the sign (positive or negative) of f(x) is ignored. This is because there is no value for the natural logarithm of negative numbers.

Properties[change | change source]

Sum of functions[change | change source]

The integral of a sum of functions is the sum of each function’s integral. that is,

${displaystyle int limits _{a}^{b}[f(x)+g(x)],dx=int limits _{a}^{b}f(x),dx+int limits _{a}^{b}g(x),dx}$

The proof of this is straightforward: The definition of an integral is a limit of sums. Thus

${displaystyle int limits _{a}^{b}[f(x)+g(x)],dx=lim _{nto infty }sum _{i=1}^{n}left(f(x_{i}^{*})+g(x_{i}^{*})right)}$

${displaystyle =lim _{nto infty }sum _{i=1}^{n}f(x_{i}^{*})+sum _{i=1}^{n}g(x_{i}^{*})}$

${displaystyle =lim _{nto infty }sum _{i=1}^{n}f(x_{i}^{*})+lim _{nto infty }sum _{i=1}^{n}g(x_{i}^{*})}$

${displaystyle =int limits _{a}^{b}f(x),dx+int limits _{a}^{b}g(x),dx}$

Note that both integrals have the same limits.

Constants in integration[change | change source]

When a constant is in an integral with a function, the constant can be taken out. Further, when a constant c is not accompanied by a function, its value is c * x. That is,

${displaystyle int limits _{a}^{b}cf(x),dx=cint limits _{a}^{b}f(x),dx}$

and

This can only be done with a constant.

${displaystyle int limits _{a}^{b}c,dx=c(b-a)}$

Proof is again by the definition of an integral.

Other[change | change source]

If a, b and c are in order (i.e. after each other on the x-axis), the integral of f(x) from point a to point b plus the integral of f(x) from point b to c equals the integral from point a to c. That is,^[3]

${displaystyle int limits _{a}^{b}f(x),dx+int limits _{b}^{c}f(x),dx=int limits _{a}^{c}f(x),dx}$

if they are in order. (This also holds when a, b, c are not in order if we define

${displaystyle textstyle int limits _{a}^{b}f(x),dx=-int limits _{b}^{a}f(x),dx}$

${displaystyle int limits _{a}^{a}f(x),dx=0}$

This follows the fundamental theorem of calculus (FTC):

${displaystyle int limits _{a}^{b}f(x),dx=-int limits _{b}^{a}f(x),dx}$

Again, following the FTC:

[change | change source]

Contour integral
Multiple integral
Numerical integration
Riemann sum
Surface integral

References[change | change source]

↑ ^1.0 ^1.1 «List of Calculus and Analysis Symbols». Math Vault. 2020-05-11. Retrieved 2020-09-18.
↑ Weisstein, Eric W. «Integral». mathworld.wolfram.com. Retrieved 2020-09-18.
↑ ^3.0 ^3.1 ^3.2 ^3.3 ^3.4 «Integral calculus — Encyclopedia of Mathematics». encyclopediaofmath.org. Retrieved 2020-09-18.
↑ ^4.0 ^4.1 Barton, David; Stuart Laird (2003). «16». Delta Mathematics. Pearson Education. ISBN 0-582-54539-0.

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Adjective

I do know that shoot-’em-ups (and saw-’em-ups) are likely to remain part of our lives, and that suggests a depressing idea: Maybe the love of violence is an integral part of human nature …

—Stephen King, Entertainment Weekly, 12 Oct. 2007

Stuffed with peanut butter, celery is the quintessential after-school snack; diced, it provides an essential crunch to chicken and potato salads; buttered up, it is an integral part of Thanksgiving stuffing.

—Sara Dickerman, New York Times Magazine, 3 Sept. 2006

Sitting out on the grass … watching the freight trains roll by on the levee at two in the morning, drinking a beer and listening to the music drifting out of the club, is an integral part of the whole experience.

—Tom Piazza, Why New Orleans Matters, 2005

She had become an integral part of their lives.

a car dealer respected for his integral honesty and straightforwardness with customers

Noun

The main tools used in the study of these functions are those we have already discussed: representation as integrals, power-series expansions, and differential equations.

—Robert S. Strichartz, The Way of Analysis, 2000

Recent Examples on the Web

Overview The Chevy Silverado 1500 pickup’s capacity for hard work is hereditary, an integral part of its family DNA.

—Eric Stafford, Car and Driver, 6 Apr. 2023

All three have been contacted about jobs elsewhere that pay more and could quickly gut an integral part of SDSU’s success while complicating their current recruiting efforts in the transfer portal.

—Mark Zeigler, San Diego Union-Tribune, 6 Apr. 2023

Accordingly, Erogbogbo’s plan for his first bricks-and-mortar restaurant began to take shape and both jollof rice and bowls would play an integral part.

—Stephanie Breijo, Los Angeles Times, 5 Apr. 2023

Many centenarians have also laid down generational roots and remain an integral part of the city’s history.

—Alexa Mikhail, Fortune Well, 2 Apr. 2023

Eduardo Díaz, deputy director of the National Museum of the American Latino at the Smithsonian Institution, said Saturday that Rodriguez-Díaz will be remembered as a integral part of San Antonio’s Latino art scene.

—Gabriella Ybarra, San Antonio Express-News, 1 Apr. 2023

While the perfect pit stop is a team effort, the wheel guns are an integral part of making wheel changes fast, reliable, and safe.

—Matt Crisara, Popular Mechanics, 30 Mar. 2023

Since her earliest memories, the dusty baseball diamonds of Queens, New York, were an integral part of Pichardo’s life.

—Meg Oliver, CBS News, 29 Mar. 2023

Cecilia Bembibre, a lecturer at the UCL Institute for Sustainable Heritage, said preserving the scent of the library was important because the smell was an integral part of its identity.

—Katie Hunt, CNN, 27 Mar. 2023

The trick is to expand the integral from one to two dimensions.

—Rhett Allain, WIRED, 14 Mar. 2023

The oracular formula is known as the Feynman path integral.

—Quanta Magazine, 6 Feb. 2023

The cutoff independent physics, defined by the Euclidean functional integral over the 4-sphere admits only a finite number of instantons.

—Sean Carroll, Discover Magazine, 29 Aug. 2012

The path integral is a way of describing a particle’s travels in terms of a quantum superposition of all possible routes.

—Ahmed Almheiri, Scientific American, 17 Aug. 2022

However, the real winners are the individuals, creators and brands making this integral to their business model(s).

—Nathaniel Hunter, Forbes, 15 July 2022

Both Croot and Bloom broke the integral into parts and proved that one main term was large and positive, and that all the other terms (which could sometimes be negative) were too small to make a meaningful difference.

—Quanta Magazine, 9 Mar. 2022

The path integral is more of a physics philosophy than an exact mathematical recipe.

—Charlie Wood, Wired, 4 July 2021

The path integral is more of a physics philosophy than an exact mathematical recipe.

—Charlie Wood, Wired, 4 July 2021

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These examples are programmatically compiled from various online sources to illustrate current usage of the word ‘integral.’ Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

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