integral examples

USAGE SUMMARY

The phrase "integral examples" is correct and usable in written English. You can use it when referring to examples that are essential or fundamental to a particular concept or argument. For example, "The study provided integral examples of how climate change affects biodiversity." Alternative expressions include "essential examples," "crucial examples," and "fundamental examples."

✓ Grammatically correct

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Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

Fig. 8 Horizontal and vertical projective integral example.

EURASIP Journal on Image and Video Processing

Also, it is possible to construct FAC by means of Erdeyi-Kober fractional integral for example or hyperdifferential non-local operators.

Journal of Theoretical and Applied Physics

Calculate the hyper-singular integral of Example 4.1 with (g(x)=x^{4}+1) and the exact value of this finite-part integral is bigl(I(g bigr) (t)=4t^{2}+2t+frac{4}{ 3} frac{t+1}{t(t-1)}+4t^{3}lnfrac{t+1}{t t-1

Journal of Inequalities and Applications

It is noted that the behavior of the modifier in Equation 5 depends not only on the detection location of P x,z) but also on the dimension parameters of the slits b and d because they are coupled in the argument of the Fresnel integral, for example, u 1 = 1 / π c z - d - b - x, and the plasmon phase term exp ik sp ⋅2d) is related with d too.

Nanoscale Research Letters

Whilst regular references were made to 'Craft' and 'Medicine' students during sessions, given this was integral, for example, to the approach to pairing students for collaborative drawing activity, great care was taken to avoid any sense of enforcing specific subject-defined identities.

BMC Medical Education

Remark 2.5 The results of this paper can be given for more general time-scale integrals, for example, Lebesgue time-scale integrals in [19] or even multiple Lebesgue time-scale integrals in [20].

Journal of Inequalities and Applications

The number of needed function evaluations depends on the cubature rule applied to compute the projection integrals, for example using a Gaussian cubature tensor product rule we need ( s + 1 ) n function evaluations per timestep of the time integration method.

Journal of Mathematics in Industry

After some preliminaries and summarization of previous known results in Section 2, Section 3 deals with a Barnes-Godunova-Levin type inequality for the Sugeno integral, and some examples are given to illustrate the results.

Journal of Inequalities and Applications

The map gis compact integral operator ([22], Example 2, p. 277).

EURASIP Journal on Advances in Signal Processing

A lot of authors presently are working on inequalities involving fractional integral operators, for example the versions of Riemann-Liouville, Caputo, Hillfer, Canvati etc.

Journal of Inequalities and Applications

Many mathematicians applied fixed point methods to the existence of unique solutions to non-linear integral equations, for example, refer to [3, 4, 9, 13 16].

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using the phrase "integral examples", ensure that the examples you are providing are indeed essential and fundamental to the concept you are illustrating. Use this phrase to emphasize the core or necessity of these examples.

Common error

Avoid using "integral examples" for examples that are merely supportive or illustrative but not fundamentally essential to understanding the topic. Overusing the term diminishes its impact.

Linguistic Context

The phrase "integral examples" functions as a noun phrase, where "integral" modifies "examples". It denotes examples that are essential or fundamental to a particular subject or concept. Ludwig AI indicates this phrase is grammatically correct.

Expression frequency: Missing

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Ludwig's WRAP-UP

In summary, "integral examples" refers to essential or fundamental examples crucial for understanding a concept. Ludwig AI confirms the phrase is grammatically sound. While the phrase itself is correct, its impact lies in the careful selection of examples that are truly indispensable. Consider related phrases like ""essential examples"" or "key examples" for nuanced variations. Due to the lack of examples for "integral examples", it's crucial to ensure the examples are indeed fundamental and not loosely related.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

essential examples

Replaces "integral" with "essential", emphasizing the necessity of the examples.

key examples

Substitutes "integral" with "key", highlighting the importance of the examples.

crucial examples

Replaces "integral" with "crucial", stressing the decisive nature of the examples.

fundamental examples

Substitutes "integral" with "fundamental", indicating the foundational nature of the examples.

indispensable examples

Replaces "integral" with "indispensable", emphasizing the examples are necessary.

significant examples

Substitutes "integral" with "significant", highlighting the importance of the examples.

important examples

Replaces "integral" with "important", indicating the relevance of the examples.

primary examples

Substitutes "integral" with "primary", emphasizing the examples are fundamental or of first importance.

notable examples

Replaces "integral" with "notable", highlighting the prominence of the examples.

central examples

Substitutes "integral" with "central", emphasizing the examples are essential and important.

FAQs

How can I use "integral examples" in a sentence?

You can use "integral examples" to highlight examples that are crucial for understanding a concept. For instance, "The study provided "essential examples" of how climate change affects biodiversity."

What can I say instead of "integral examples"?

You can use alternatives like ""essential examples"", "key examples", or "crucial examples" depending on the context.

Which is correct, "integral examples" or "integrated examples"?

"Integral examples" refers to examples that are essential, while "integrated examples" describes examples that are combined or incorporated. The correct choice depends on the intended meaning.

What's the difference between "integral examples" and "important examples"?

"Integral examples" emphasizes that the examples are fundamental and essential, whereas "important examples" simply suggests that the examples are significant or relevant but not necessarily indispensable.