more general integral

USAGE SUMMARY

The phrase "more general integral" is correct and usable in written English.
It can be used in mathematical contexts when discussing integrals that encompass a broader range of cases or applications. Example: "In this paper, we will explore the concept of the more general integral, which allows for greater flexibility in solving complex equations."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

9 human-written examples

Firstly, we have more general integral boundary conditions.

Boundary Value Problems

In recent past, several authors (e.g., [22 26]) proved various fixed point theorems employing relatively more general integral type contractive conditions.

Fixed Point Theory and Applications

To overcome the weakness, in this paper we avoid the above-mentioned conditions and use another concise assumption to discuss some more general integral inequalities of Wendroff type.

Journal of Inequalities and Applications

The asymptotic result, though reasonably tame, presents new difficulties when we consider a more general integral, and this is circumvented here by the proof of two new inequalities.

Journal of Inequalities and Applications

In this section we consider the question of obtaining upper and lower bounds for the more general integral, namely (int_{-infty}^{infty }frac{vert sin xvert ^{alpha}}{ vert xvert ^{beta}}, dx).

Journal of Inequalities and Applications

In this paper, motivated by the work above, we will establish the following much more general integral inequality: u ( x, y ) ≤ a ( x, y ) + ∑ n = 1 2 ∫ b n ( x 0 ) b n ( x ) ∫ c n ( y o ) c n ( y ) f n ( x, y, s, t ) ω n ( u ( s, t ) ) d s d t + g ( x, y ) ∑ ( x 0, y 0 ) < ( x i, y i ) < ( x, y ) β i u m ( x i − 0, y i − 0 ), m > 0, (1.8).

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

51 human-written examples

When more general integrals are considered (e.g. the Moore-Pollard integral, cf. [1], p.263), we may weaken this assumption and assume that f and g have no common one-sided discontinuities.

Journal of Inequalities and Applications

Extensions to the case of more general of integral equations are left for future studies.

Mathematical Sciences

However, regarding Eq. (36), the VIM transforms it into a more general Volterra integral equation from which one can obtain approximate solutions of higher accuracies.

Advances in Difference Equations

Especially, stimulated by the work of Ait Dads, Cieutat, and Lhachimi [5], the authors in [8] investigated the existence of positive pseudo almost periodic solution for the following more general neutral integral equation: x t)=alpha(t) x t-beta)+ int^{t}_{-infty}a(t,t-s)fbigl(s,x t-beta),ds,quad tin mathbb{R}.

Advances in Difference Equations

A slightly improved de-singularity approach has been used by Ma and Yang [6] to study a more general singular integral inequality as follows: u ( t ) ≤ a ( t ) + b ( t ) ∫ 0 t ( t σ − s σ ) μ − 1 s γ − 1 g ( s ) u ( s ) d s + c ( t ) ∫ 0 t ( t σ − s σ ) μ − 1 s γ − 1 g ( s ) w ( u ( s ) ) d s. (1.2).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When discussing mathematical concepts, clearly define the specific properties that make the "more general integral" distinct from other types. This helps avoid ambiguity and ensures clarity in technical writing.

Common error

Avoid using "more general integral" without specifying what aspects are being generalized. Always provide context or examples to illustrate the extended applicability or features of the integral.

Linguistic Context

The phrase "more general integral" functions as a noun phrase, where "more general" acts as a pre-modifying adjective specifying the type of integral. As Ludwig AI confirms, this phrase is used to denote an integral that encompasses a broader range of cases.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

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Ludwig's WRAP-UP

The phrase "more general integral" is a noun phrase primarily used within scientific and academic contexts to describe integrals with broader applications or relaxed conditions. As Ludwig AI validates, the phrase is grammatically correct and frequently appears in research articles related to mathematical analysis. While alternatives like "broader integral" or "generalized integral" exist, this specific phrasing effectively communicates the extended scope of the integral in question. Remember to clearly define the generalized properties to ensure precision in technical writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

broader integral

This alternative uses a simpler adjective to convey the expanded scope.

generalized integral

This alternative emphasizes the process of generalizing the integral.

more encompassing integral

This alternative highlights the inclusive nature of the integral.

more inclusive integral

This option stresses the property of including diverse cases.

wider integral

This alternative uses a simpler adjective referring to a larger scope.

more extensive integral

This option places emphasis on the range or reach of the integral.

more comprehensive integral

This alternative underlines the all-inclusive characteristics of the integral.

more expansive integral

This version focuses on the expanded nature of the integral.

more universal integral

This option suggests the integral has broader applicability.

more overarching integral

This alternative conveys the integral's high-level or comprehensive role.

FAQs

What does "more general integral" mean in mathematics?

In mathematics, "more general integral" refers to an integral that applies to a broader class of functions or situations than a standard or specific integral. It often involves relaxing certain conditions or extending the definition of integration.

How does a "more general integral" differ from a standard integral?

A "more general integral" differs from a standard integral by encompassing a wider range of functions, integration methods, or conditions. This might involve handling singularities, unbounded intervals, or more complex functions.

What are some alternatives to saying "more general integral"?

Some alternatives include "broader integral", "generalized integral", or "more encompassing integral", depending on the specific context you want to emphasize.

In what contexts would I use the term "more general integral"?

You would use "more general integral" when discussing extensions or generalizations of integration methods in mathematical analysis, such as in research papers, textbooks, or advanced mathematical discussions.