the representation, usually in symbolic form, of the difference in values of a primitive of a given function evaluated at two designated points.
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Compare indefinite integral.
Origin of definite integral
First recorded in 1875–80
Words nearby definite integral
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2020
British Dictionary definitions for definite integral
- the evaluation of the indefinite integral between two limits, representing the area between the given function and the x- axis between these two values of x
- the expression for that function, ʃ b a f (x) dx, where f (x) is the given function and x = a and x = b are the limits of integration. Where F (x) = ʃ f (x) dx, the indefinite integral, ʃ b a f (x) dx = F (b) –F (a)
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
Scientific definitions for definite integral
[ dĕf′ə-nĭt ]
The difference between the values of an indefinite integral evaluated at each of two limit points, usually expressed in the form ∫baƒ(x)dx. The result of performing the integral is a number that represents the area bounded by the curve of ƒ(x) between the limits and the x-axis if f(x) is greater than or equal to zero between the limits.
The result of an integration performed on a fixed interval.
The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.