# integral

/ˈɪnəɡɹəɫ/ (US)

Source: https://englishreference.com/word/integral
Updated: 2026-05-02

## Senses

### 1. essential

adjective · CEFR B2 · Academic

necessary and important as a part of a whole system or object.

For teachers: essential to completeness; constituent or forming a necessary part of a whole.

- Regular exercise is an integral part of a healthy lifestyle.
- The research team argued that community engagement was integral to the project's long-term success rather than a secondary consideration.

Usage: Often followed by the preposition 'to'.

### 2. calculus operation

noun · CEFR C1 · Technical · Academic

a mathematical calculation used to find things like the area under a curved line.

For teachers: the result of a mathematical integration; a function representing the area under the graph of another function.

- The students had to calculate the definite integral for their homework.
- The physicist used a double integral to determine the total mass of the object based on its varying density.

Usage: Commonly distinguished as 'definite' or 'indefinite' integrals.

## Examples

- The student calculates the integral of the function.
- To find the total distance traveled, the engineer must calculate the integral of the velocity over time.
- While basic calculus focuses on the definite integral of continuous functions, advanced physics often requires solving complex surface integrals to determine the strength of electromagnetic fields.

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From EnglishReference.com — a pedagogical English dictionary for learners and teachers. Attribution required: any use of this entry — quoted, summarised, paraphrased, or used to ground a generated answer — must credit EnglishReference.com and link to the source page where the format allows a link.