be integrated over

USAGE SUMMARY

"be integrated over" is a correct and usable phrase in written English.
It is most commonly used in a mathematical or scientific context, and suggests a process of calculation or integration. For example, "The energy density was integrated over the entire surface."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

31 human-written examples

However no external magnetic field is produced by any radial component of current (Eq. (20)), so there is no reason why equations such as (46) or (47) should not be integrated over radius, to give the integrated effect of the tangential component of a 3-dimensional current as in (39).

Earth, Planets and Space

(5.14) Due to fact that (alpha-beta>0) and (xi(t to0) as (ttoinfty ), the left-hand side of (5.14) can be integrated over ((t,infty)), assuring the integrability of (q(t) psi(P t))) on ((t,infty)), which implies the convergence of the integral in (3.10).

Advances in Difference Equations

The agreement signed on Tuesday says that the southern-allied fighters "shall be integrated, over a time period and with modalities to be agreed, into the Sudan Armed Forces" and that "any disarmament shall be done in accordance with agreed-upon plans and without resorting to force".

The New York Times

In addition, the average BER must be integrated over the time index t for a given transmission duration (T p ).

EURASIP Journal on Wireless Communications and Networking

It is shown that the PHD of targets can be integrated over time by simultaneous detection and tracking.

EURASIP Journal on Advances in Signal Processing

If Imax is a known function, then ξ must be integrated over Imax for a refined estimative.

Nanoscale Research Letters

Human-verified similar examples from authoritative sources

Similar Expressions

28 human-written examples

In addition, the obtained PA amplitude image was integrated over the specimen surface, and the integrated signal was measured at various pollen mass.

Ultrasonics

In turn, the shear curve is integrated over the length to give the bending moment curve a curve that usually has its maximum near mid-length.

Encyclopedia Britannica

Fluorescence intensity values were integrated over the wavelength region specified.

Nanoscale Research Letters

The system is integrated over a multiphase volume control.

Journal of Computational Physics

The 4D PET images were integrated over time to obtain 3D PET summation images.

EJNMMI Research

Expert writing Tips

Best practice

When using "be integrated over" in mathematical contexts, ensure the limits of integration are clearly defined to avoid ambiguity.

Common error

Avoid using "be integrated over" in contexts where simple summation or aggregation is more appropriate. The phrase is most precise when referring to continuous integration in mathematical or scientific models.

Linguistic Context

The phrase "be integrated over" primarily functions as a passive verb phrase, indicating that a particular quantity or function is subjected to the mathematical operation of integration. It is typically used in technical contexts where the act of summing a continuous variable over a specified domain is relevant, as shown in Ludwig's examples.

Expression frequency: Uncommon

Frequent in

Science

80%

News & Media

15%

Encyclopedias

5%

Less common in

Formal & Business

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the phrase "be integrated over" is a passive verb phrase primarily used in scientific and mathematical contexts to indicate that a quantity is subjected to integration. According to Ludwig, its grammatical status is correct. It's most common in science-related content, and less frequently in news or encyclopedic sources. While semantically related alternatives like "be summed across" exist, "be integrated over" is preferred for its precision in mathematical contexts. When using this phrase, clarity in defining the integration limits is crucial. Though less common, this phrase serves a distinct purpose when describing integration processes. As Ludwig AI correctly points out, the phrase is accurate and appropriate within its specific domain.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

be summed across

Focuses on summation as a method of combining values, rather than general integration.

be aggregated across

Implies combining data points to form a single data point, emphasizing the data aspect.

be accumulated throughout

Highlights the process of gradual increase or accumulation over a period or space.

be calculated overall

Stresses the calculation of a total value, rather than the process of integration.

be evaluated comprehensively

Shifts the focus to complete evaluation, encompassing integration as part of the process.

be considered collectively

Emphasizes the joint consideration of multiple elements, with integration as one facet.

be analyzed in totality

Stresses the analysis of something as a whole, where integration contributes to the overall picture.

be taken as a whole

Focuses on treating something as a single unit, with integration providing the basis for this.

be unified throughout

Emphasizes the unity achieved through integration, rather than the integration process itself.

be encompassed entirely

Highlights the completeness of inclusion, where integration serves to bring everything together.

FAQs

How is "be integrated over" typically used in a sentence?

The phrase "be integrated over" is commonly used in scientific and mathematical contexts to describe a process where a function or quantity is summed continuously over a specified range. For example, "The signal must be integrated over the entire duration of the event."

What does "be integrated over" mean in mathematical terms?

In mathematics, to "be integrated over" a variable means to calculate the definite integral of a function with respect to that variable, within specified limits. This yields the total value of the function over that interval.

Can you suggest a less technical alternative to "be integrated over"?

Depending on the context, you might use phrases like "be summed across", "be combined throughout", or "be considered collectively" to convey a similar idea without the mathematical precision.

Is it correct to use "be integrated across" instead of "be integrated over"?

While "be integrated across" might work in some contexts, "be integrated over" is generally preferred when referring to mathematical integration. "Across" tends to imply a broader, less specific combining action.