INTEGRALS Meaning and
Definition
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Integrals can be defined as mathematical entities used to quantify the accumulation of a quantity over a region or a specific interval. In mathematics, an integral allows for the calculation of the area under a curve, the length of a curve, the volume of a solid, or the total accumulation of a function. The process of calculating an integral is known as integration.
An integral is represented by a symbol ∫ (known as the integral sign) with the function to be integrated written after it. The integral is equivalent to the antiderivative (or the reverse process of differentiation) of the function. It involves dividing the region into infinitesimally small sections and summing up the contributions of each section to obtain the overall value.
There are two types of integrals: definite and indefinite. A definite integral is used to find the exact accumulation of a quantity between two given points or over a specific interval. It produces a numerical value as the result. On the other hand, an indefinite integral does not have specific boundaries and yields a general function, or a family of functions, known as the antiderivative.
Integrals play a crucial role in various branches of mathematics and physics, enabling the calculation of areas, volumes, and probabilities. They are extensively used in calculus, engineering, economics, and other fields that require the analysis and quantification of continuous quantities.
Common Misspellings for INTEGRALS
Etymology of INTEGRALS
The word "integral" has its origins in Latin. It comes from the Latin word "integralis", which means "whole" or "complete". The term first appeared in English in the early 17th century, specifically in the mathematical context, referring to the concept introduced by mathematician John Wallis. Wallis defined the integral as the inverse process of differentiation, and the term "integral" eventually became associated with the operation of finding the integral of a function.
Similar spelling words for INTEGRALS
- integrally,
- integrator,
- indexer,
- integrating,
- integrated,
- integrative,
- integer,
- integrity,
- integrate,
- integration,
- integral,
- integumental,
- indexical.
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