indefinite integral

American  

noun

Mathematics.

1. a representation, usually in symbolic form, of any function whose derivative is a given function.

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indefinite integral British  

noun

1. maths

   1. any function whose derivative is the given function, as x ², x ² + 3, x ²–5, etc of 2x

   2. the schema representing all such functions, here x ² + k

   3. the symbolic representation of this as a function of the given function, written ʃ f ( x ) dx where f ( x ) is the given function

   4. the symbol ʃ

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indefinite integral Scientific  

/ ĭn-dĕf′ə-nĭt /

1. A function whose derivative is a given function.

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Etymology

Origin of indefinite integral

First recorded in 1875–80

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• definite integral vs. indefinite integral

Example Sentences

Use substitution to evaluate the indefinite integral ∫ 3x2 e2x3 dx.

From Textbooks • Mar. 30, 2016

Evaluating the derivative and indefinite integral in this way is called term-by-term differentiation of a power series and term-by-term integration of a power series, respectively.

From Textbooks • Mar. 30, 2016

An indefinite integral is a family of functions.

From Textbooks • Mar. 30, 2016

Since the indefinite integral of a vector-valued function involves indefinite integrals of the component functions, each of these component integrals contains an integration constant.

From Textbooks • Mar. 30, 2016

It will therefore allow of registering a set of values of ∫ax ydx for any values of x, and thus of tabulating the values of any indefinite integral.

From Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" by Various