Integrate: meaning, definitions and examples

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integrate

[ˈɪntɪɡreɪt ]

Definition

^{Context #1 | Verb}

mathematics

To find the integral of a function over a given interval. It involves finding the area under the curve of the function.

Synonyms

calculate the integral, find the antiderivative.

Which Synonym Should You Choose?

Word	Description / Examples
integrate	This word is commonly used in mathematical contexts, particularly in calculus, where it refers to the process of finding the integral of a function. It can also be used metaphorically in everyday language to mean combining parts into a whole. In calculus class, we learned how to integrate various functions The new software helps to integrate different data sources seamlessly
calculate the integral	This phrase is used specifically in mathematical situations where one needs to find the definite or indefinite integral of a function. It emphasizes the process of calculation. To solve the area under the curve, first calculate the integral of the function from point A to point B In the exam, we had to calculate the integral of a polynomial function
find the antiderivative	Used in mathematics, specifically in calculus, this phrase focuses on finding the original function whose derivative is given. It is more formal and technical. Given the derivative, we need to find the antiderivative to solve this problem Finding the antiderivative is crucial in solving differential equations

Word

Description / Examples

integrate

This word is commonly used in mathematical contexts, particularly in calculus, where it refers to the process of finding the integral of a function. It can also be used metaphorically in everyday language to mean combining parts into a whole.

In calculus class, we learned how to integrate various functions
The new software helps to integrate different data sources seamlessly

calculate the integral

This phrase is used specifically in mathematical situations where one needs to find the definite or indefinite integral of a function. It emphasizes the process of calculation.

To solve the area under the curve, first calculate the integral of the function from point A to point B
In the exam, we had to calculate the integral of a polynomial function

find the antiderivative

Used in mathematics, specifically in calculus, this phrase focuses on finding the original function whose derivative is given. It is more formal and technical.

Given the derivative, we need to find the antiderivative to solve this problem
Finding the antiderivative is crucial in solving differential equations

Examples of usage

We need to integrate the function f(x) over the interval [a, b].
Integrating this function will give us the total area under the curve.

Interesting Facts

Etymology

The word comes from the Latin 'integrare', meaning 'to make whole' or 'to renew'.
In English, it first appeared in the late 14th century, reflecting the idea of making things complete.

Education

In teaching, integrating subjects helps students learn by connecting lessons, like math with art.
Curriculum integration promotes teamwork among teachers to provide a cohesive learning experience.

Technology

In computing, integration refers to combining software or systems to work together efficiently.
APIs (Application Programming Interfaces) facilitate integration between different software applications.

Sociology

Social integration involves bringing diverse groups together in communities for better coexistence.
Policies promoting social integration aim to reduce barriers and improve equality among different cultural groups.

Mathematics

In calculus, integration is a mathematical technique that finds the total area under a curve.
It’s the reverse process of differentiation, which means breaking down functions into simpler parts.

Translations

Translations of the word "integrate" in other languages:

🇵🇹 integrar

🇮🇳 एकीकृत करना

🇩🇪 integrieren

🇮🇩 mengintegrasikan

🇺🇦 інтегрувати

🇵🇱 integrować

🇯🇵 統合する

🇫🇷 intégrer

🇪🇸 integrar

🇹🇷 entegre etmek

🇰🇷 통합하다

🇸🇦 دمج

🇨🇿 integrovat

🇸🇰 integrovať

🇨🇳 整合

🇸🇮 integrirati

🇮🇸 samþætta

🇰🇿 интеграциялау

🇬🇪 ინტეგრირება

🇦🇿 birləşdirmək

🇲🇽 integrar

Word Frequency Rank

Position #7,743 indicates this is an advanced-level word. While not essential for basic communication, it will enhance your ability to understand and create more nuanced content.

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7740 ecology
7741 designers
7742 gambling
7743 integrate
7744 dissemination
7745 graded
7746 affirm
...