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- Dictionaryintegral
adjective
- 1. necessary to make a whole complete; essential or fundamental: "games are an integral part of the school's curriculum" Similar Opposite
- 2. of or denoted by an integer.
noun
- 1. a function of which a given function is the derivative, i.e. which yields that function when differentiated, and which may express the area under the curve of a graph of the function.
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Learn the meaning of integral as an adjective, noun, and mathematical term. Find out how to use integral in sentences and compare it with related words and phrases.
- English (US)
INTEGRAL meaning: 1. necessary and important as a part of a...
- Traditional
INTEGRAL translate: 構成整體所必需的, 內置的. Learn more in the...
- Simplified
INTEGRAL translate: 构成整体所必需的, 内置的. Learn more in the...
- Znaczenie Integral, Definicja W Cambridge English Dictionary
integral definicja: 1. necessary and important as a part of...
- English (US)
e. In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [a] the other being differentiation.
Learn the meaning of integral as an adjective and a noun in mathematics and other contexts. See synonyms, examples, word history, and related phrases of integral.
Nov 16, 2022 · Learn how to define and evaluate definite integrals using limits, summation, and properties. See examples, explanations, and proofs of various integral properties.
- Notation
- Definite Integral
- Positive Area
- Continuous
- Properties
- Summary
- GeneratedCaptionsTabForHeroSec
The symbol for "Integral" is a stylish "S" (for "Sum", the idea of summing slices): And then finish with dxto mean the slices go in the x direction (and approach zero in width).
A Definite Integral has start and end values: in other words there is an interval[a, b]. a and b (called limits, bounds or boundaries) are put at the bottom and top of the "S", like this: We find the Definite Integral by calculating the Indefinite Integral at a, and at b, then subtracting: Notation: It is usual to show the indefinite integral (with...
But sometimes we want all area treated as positive(without the part below the axis being subtracted). In that case we must calculate the areas separately, like in this example:
Oh yes, the function we are integrating must be Continuous between a and b: no holes, jumps or vertical asymptotes (where the function heads up/down towards infinity).
Area above − area below
The integral adds the area above the axis but subtracts the area below, for a "net value":
Adding Functions
The integral of f+g equals the integral of f plus the integral of g:
Reversing the interval
Reversing the direction of the interval gives the negative of the original direction.
The Definite Integral between a and b is the Indefinite Integral at b minus the Indefinite Integral ata.
Learn how to use the integral symbol to find the area under a function's graph between two values. See examples, rules, notation and properties of definite integrals.
Learn how to use integration to find areas, volumes, central points and more. Integration is the reverse of differentiation and involves adding up slices of a function.
Aug 17, 2024 · State the definition of the definite integral. Explain the terms integrand, limits of integration, and variable of integration. Explain when a function is integrable.
