DEFINITE INTEGRAL Meaning and
Definition
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The definite integral is a mathematical tool used in calculus to calculate the area under a curve between two given values, known as the limits of integration. It is denoted by the symbol ∫, and has both a function to be integrated and the limits specified. The definite integral represents the accumulation of infinitesimally small areas under the curve within the given range.
To evaluate a definite integral, the process of integration is applied to determine the antiderivative of the function with respect to the independent variable. This antiderivative is then evaluated at the upper and lower limits of integration, and their difference provides a numerical value for the area between the curve and the x-axis within the specified interval.
The definite integral provides a more precise measure of area than the indefinite integral (also known as the antiderivative), which represents a family of functions that could result from the original function. It enables the calculation of area even for functions that are not solely positive, as it considers the differences between positive and negative areas. Furthermore, the definite integral can be used to calculate other quantities such as the net change of a function or the average value of a function.
In addition to its applications in measuring areas under curves, the definite integral is also utilized in numerous fields such as physics, economics, and engineering to determine quantities such as work, displacement, and probability density.
Common Misspellings for DEFINITE INTEGRAL
- sefinite integral
- xefinite integral
- cefinite integral
- fefinite integral
- refinite integral
- eefinite integral
- dwfinite integral
- dsfinite integral
- ddfinite integral
- drfinite integral
- d4finite integral
- d3finite integral
- dedinite integral
- decinite integral
- devinite integral
- deginite integral
- detinite integral
- derinite integral
- defunite integral
Etymology of DEFINITE INTEGRAL
The word integral comes from the Latin word integralis, which means whole or entire. The term definite in definite integral emphasizes that the integral is taken over a specific interval or range of values rather than an indefinite one. The term definite integral was introduced by the mathematician Joseph Fourier in the early 19th century to distinguish it from the concept of the indefinite integral, which was previously known as the integral calculus.
Similar spelling words for DEFINITE INTEGRAL
