# indefinite integral

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## indefinite integral

n. Mathematics
A function whose derivative is a given function. Also called antiderivative.

## indefinite integral

n
(Mathematics) maths
a. any function whose derivative is the given function, as x2, x2 + 3, x2–5, etc of 2x
b. the schema representing all such functions, here x2 + k
c. the symbolic representation of this as a function of the given function, written ∫f(x)dx where f(x) is the given function
d. the symbol ∫

## indef′inite in′tegral

n.
a representation of any function whose derivative is a given function.
[1875–80]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 indefinite integral - the set of functions F(x) + C, where C is any real number, such that F(x) is the integral of f(x)integral - the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
Translations
neodređeni integral

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obtained necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative and indefinite integral. There has been a significant development in ordinary and partial fractional differential equations in recent years [6-9].
As the screen suggests, this particular device represents an indefinite integral by leaving blanks where the limits of a definite integral might appear.
For example int(S x) is the indefinite integral of S with respect to 'x'.
Then applying an indefinite integral of the Bessel function (see [30, Page 35])
To develop analytical expressions for inductances, the effective inverse air gap function of the eccentric SPSM has been defined, and its indefinite integral has then been determined.
the indefinite integral in the right hand side of (2.7) involving the arbitrary constant [c.sub.0] [member of] C.
He was especially impressed, as a young boy, to see an indefinite integral among the 1 + 1 = 2's on the board in Huey, Dewey, and Louie's kindergarten class!)
(1) In what conditions the curvilinear indefinite integral (primitive) of a closed Lagrangian 1-form is also a Lagrangian?
Baturo); (33) Exploring Students' Mathematics-Related Self Image as Learners (Silvana Martins Melo and Marcia Maria Fusaro Pinto); (34) Difficulties on Understanding the Indefinite Integral (N.
Both simple examples (such as creating a function which is the sum of two functions given as parameters, or creating the composition of two functions) and more complex examples such as generating a function representing the a finite number of terms of a Fourier series given the coefficients, and generating a function which is an approximation to an indefinite integral of a given function are shown.
The first approach is to find an inclusion of the integrand, then integrate this inclusion to obtain an inclusion of the indefinite integral. Inclusions for the integrand may be obtained from Taylor polynomials, Tschebyscheff polynomials, or other approximating forms which have a known error term.

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