indefinite integral

USAGE SUMMARY

The phrase "indefinite integral" is correct and usable in written English. You can use it in mathematical contexts, particularly in calculus when discussing integration without specific limits. An example is: "To find the area under the curve, we need to calculate the indefinite integral of the function." Alternative expressions include "antiderivative" and "primitive function."

✓ Grammatically correct

Science

Encyclopedias

Academia

Human-verified examples from authoritative sources

Exact Expressions

29 human-written examples

The process of finding an indefinite integral is called integration.

Britannica

This chapter provides the general rules for obtaining an indefinite integral and explains the three methods of integration: integration by substitution, integration by parts, and integration of partial fractions.

Mathematics for Chemistry & Physics

Moreover, in such a case the indefinite integral (I (t ):=int _{a}^{t}f,mathrm{d}g) reveals similar irregularity as the integrator g, namely, (sup_{delta>0}delta^{q-1} operatorname{TV}^{delta}(I,[a,b]) <infty ).

Journal of Inequalities and Applications

In the indefinite integral, another name for the antiderivative, the constant must be included).

Encyclopedia Britannica

Because the derivative of a constant is zero, the indefinite integral is not unique.

Britannica

This is called the (indefinite) integral of the function y = x2, and it is written as ∫x2dx.

Encyclopedia Britannica

Human-verified similar examples from authoritative sources

Similar Expressions

31 human-written examples

Topics include limits, continuity, the derivative, basic differentiation formulas and applications (curve-sketching, optimization, related rates), definite and indefinite integrals, the fundamental theorem of calculus.

Princeton University

Indefinite integrals are those where the determination of the constant requires additional information namely, the initial or boundary conditions associated with the physical problem involved.

Mathematics for Chemistry & Physics

In [7], Almeida exhibited the conditions of optimality for functionals depending on Caputo fractional integrals and derivatives, on indefinite integrals and on the presence of time delay.

Advances in Difference Equations

This, in view of the preceding subsection, will give us more exact results about the irregularity of the indefinite integrals (int _{a}^{cdot}f,mathrm{d}g).

Journal of Inequalities and Applications

If f belongs to K ϕ α ( D d ) Open image in new window with respect to ϕ, then we have the following formulas for definite and indefinite integrals based on DE transformation which is given and fully discussed in [18]: ∫ a b f ( x ) dx = h ∑ j = − N j = N f ( ϕ ( jh ) ) ϕ ′ ( jh ) + O ( exp ( − 2 πdN log ( 2 πdN / α ) ) ) Open image in new window (4).

Mathematical Sciences

Expert writing Tips

Best practice

When evaluating an "indefinite integral", always remember to include the constant of integration (+ C) to represent the family of all possible antiderivatives.

Common error

A common mistake is to omit the constant of integration (+ C) when finding an "indefinite integral". This omission leads to an incomplete solution, as it fails to represent the entire family of antiderivatives.

Linguistic Context

The phrase "indefinite integral" functions as a noun phrase identifying a mathematical concept. As Ludwig AI points out, it refers to a function whose derivative is a given function, also known as an antiderivative.

Expression frequency: Uncommon

Frequent in

Science

60%

Encyclopedias

20%

Academia

10%

Less common in

News & Media

5%

Wiki

5%

Formal & Business

0%

Ludwig's WRAP-UP

The phrase "indefinite integral" accurately denotes a core concept in calculus, representing the antiderivative of a function. As Ludwig AI suggests, its usage is grammatically correct and most commonly encountered in scientific, encyclopedic, and academic contexts. When working with "indefinite integrals", remember to always include the constant of integration (+ C) to account for the entire family of antiderivatives. Alternatives like "antiderivative" and "primitive function" can be used depending on the nuance you want to convey.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

antiderivative

Refers to the inverse process of differentiation, yielding a function whose derivative is the original function; emphasizes the result rather than the process.

primitive function

Similar to antiderivative, but emphasizes the function before the application of any limits or constants of integration.

integral without limits

Highlights the absence of specific bounds of integration, focusing on the general form of the integral.

symbolic integral

Emphasizes the formal, symbolic representation of the integral, particularly in computer algebra systems.

general integral

Stresses the generality of the solution, encompassing all possible antiderivatives due to the constant of integration.

family of antiderivatives

Highlights that the indefinite integral represents not a single function, but a set of functions differing only by a constant.

unspecified integral

Emphasizes that the limits of integration are not specified.

integral with arbitrary constant

Explicitly mentions the presence of an arbitrary constant in the integral's result.

function whose derivative is known

Describes the indefinite integral in terms of its fundamental relationship to differentiation.

reversed derivative

Informal way to refer to the concept of indefinite integration by inverting the differentiation.

FAQs

What is the purpose of calculating an "indefinite integral"?

Calculating an "indefinite integral" provides a general function whose derivative matches a given function. It's useful for finding antiderivatives and solving differential equations, where the constant of integration is determined by initial conditions.

How does an "indefinite integral" differ from a definite integral?

An "indefinite integral" results in a function (plus a constant), representing the family of antiderivatives. A definite integral, on the other hand, calculates the area under a curve between two specific limits, resulting in a numerical value.

What are some alternative ways to refer to an "indefinite integral"?

Alternatives to "indefinite integral" include "antiderivative" and "primitive function". These terms emphasize the function resulting from the reverse process of differentiation.

When should I use an "indefinite integral" versus a definite integral?

Use an "indefinite integral" when you need a general expression for all possible antiderivatives of a function. Use a definite integral when you need to calculate the area under a curve between two specific points.