integral from

USAGE SUMMARY

The phrase "integral from" is not correct in standard written English.
It seems to be a misphrasing, as the correct term is "integral of" when referring to the mathematical concept of integration. Example: "To find the area under the curve, we need to calculate the integral of the function from a to b."

⚠ May contain grammatical issues

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

50 human-written examples

In Limón's work the use of the back is integral from the way it connects the legs and torso to constantly curving arms, which seem to sprout from the spine allowing the body to morph seamlessly between weight and weightlessness.

The New York Times - Arts

(Stieltjes multiplicative integral (from [18])).

EPJ Quantum Technology

Denoting these samples again by, the integral from (9) can be approximated by (11).

EURASIP Journal on Wireless Communications and Networking

Now, we can derive the first integral from the transformation pair.

Advances in Difference Equations

Multiplying (4.1) on both sides by and taking integral from to, we have (4.9).

Journal of Inequalities and Applications

The global existence result follows from the integral from equation (3.2) and equation (3.3).

Boundary Value Problems

Human-verified similar examples from authoritative sources

Similar Expressions

9 human-written examples

A simple proof of the equality can be done by performing an integration by parts in the integrals from the right side and changing the variable.

Mathematical Sciences

The method that used the fracture-surface topography analysis (FRASTA) for determining J-integral from fracture surfaces of materials was introduced.

Acta Metallurgica Sinica (English Letters)

In resent years, the authors [8, 20 22] derived some formulas of q-polynomials and q-integral from studying the properties of solutions about some q-difference equations.

Advances in Difference Equations

The upper Darboux-Stieltjes Δ-integral from a to b with respect to function g is defined by ∫ a b ¯ f ( t ) Δ g ( t ) = inf P ∈ P ( I ) U Δ ( P, f, g ) ; the lower Darboux-Stieltjes Δ-integral from a to b with respect to function g is defined by ∫ a b f ( t ) Δ g ( t ) = sup P ∈ P ( I ) U Δ ( P, f, g ).

Advances in Difference Equations

If a ∈ [ 0, b ] and f is defined on the interval [ 0, b ], its q-integral from a to b is defined by ∫ a b f ( t ) d q t = ∫ 0 b f ( t ) d q t − ∫ 0 a f ( t ) d q t.

Advances in Difference Equations

Expert writing Tips

Best practice

If you are referring to something being an essential part that originates from somewhere, rephrase for better clarity. Instead of "integral from", consider "originating from" or "stemming from".

Common error

Avoid using "integral from" when describing mathematical integration. The correct term is "integral of". Using "integral from" can confuse readers and undermine the credibility of your writing.

Linguistic Context

The phrase "integral from" functions as a prepositional phrase, often intended to describe the relationship between an integral and its limits or, more broadly, to indicate origin or derivation. However, Ludwig AI indicates it's often grammatically incorrect.

Expression frequency: Common

Frequent in

Science

77%

News & Media

17%

Wiki

3%

Less common in

Formal & Business

3%

Encyclopedias

0%

Social Media

0%

Ludwig's WRAP-UP

The phrase "integral from" presents a complex case. While common, especially in scientific literature, it's often grammatically questionable. Ludwig AI highlights that in mathematical contexts, "integral of" is the correct term. When aiming to convey that something is essential and originates elsewhere, consider alternatives like "originating from" or "stemming from" for enhanced clarity. While sources using this phrase are generally authoritative, the grammatical inconsistency impacts overall writing quality, making careful consideration and potential rephrasing crucial.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

integral of

Changes the preposition to the correct form for mathematical integration.

integration from

Replaces "integral" with its noun form, maintaining a similar mathematical context.

definite integral from

Specifies the type of integral being referenced, adding clarity.

integration ranging from

Emphasizes the range over which integration occurs.

calculated from the integral

Rephrases to focus on the calculation aspect based on an integral.

crucial element originating from

Shifts focus to the originating source when discussing essential elements.

essential aspect stemming from

Highlights an aspect that is key and its origin.

key component derived from

Focuses on a vital part and how it is obtained.

inherent quality arising from

Emphasizes an inherent characteristic and its source.

vital attribute sourced from

Underscores a critical attribute and where it comes from.

FAQs

When should I use "integral of" instead of "integral from"?

Use "integral of" when referring to the mathematical concept of integration. For example, "the integral of a function" is correct, while "the integral from a function" is not. If the context is about something essential stemming from somewhere, consider alternatives.

Is "integral from" ever grammatically correct?

While "integral from" appears in some contexts, it's often misused or grammatically awkward. In most cases, rephrasing with terms like "originating from" or using "integral of" (for mathematical contexts) is better.

What are some alternatives to "integral from" when discussing essential elements?

Depending on the context, you can use phrases like "stemming from", "originating from", or "derived from" to express the idea of something essential coming from a particular source.

How can I ensure I'm using the correct phrasing with "integral"?

Double-check the context. If it's a mathematical discussion, always use "integral of". If you're describing something essential arising from something else, consider alternative phrasings to avoid ambiguity. Reviewing examples of correct usage can also help.