Integrate Meaning: Definition, Examples, and Translations
๐
integrate
[หษชntษชษกreษชt ]
Definition
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.
|
| 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.
|
| 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.
|
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.
Translations
To see the translation, please select a language from the options available.
Interesting Facts
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.
- Itโs the reverse process of differentiation, which means breaking down functions into simpler parts.
Origin of 'integrate'
Main points about word origin
- 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.
The word 'integrate' comes from the Latin word 'integratus', which means 'renewed' or 'repeated'. In mathematics, the concept of integration dates back to the 17th century, with contributions from mathematicians like Newton and Leibniz. It plays a crucial role in calculus and has applications in various fields such as physics, engineering, and economics.
See also: disintegrate, disintegrated, integratable, integrated, integrating, integration, integrative, reintegrate.