(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
Used in a Sentence
integrals
Definitions, parts of speech, synonyms, and sentence examples for integrals.
Editorial note
In quantum field theory you frequently do integrals in 4-ϵ as a way of regularizing divergent integrals.
Examples16
Definitions4
Parts of speech1
Quick take
(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
Meaning at a glance
The clearest senses and uses of integrals gathered in one view.
(space science, ESA) Abbreviation of International Gamma-Ray Astrophysics Laboratory (a satellite of the European Space Agency).
(mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.
Definitions
Core meanings and parts of speech for integrals.
noun
(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
noun
(space science, ESA) Abbreviation of International Gamma-Ray Astrophysics Laboratory (a satellite of the European Space Agency).
noun
(mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.
noun
(mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.
Example sentences
In quantum field theory you frequently do integrals in 4-ϵ as a way of regularizing divergent integrals.
The fact that we can build everything from set theory doesn't mean we don't need to know about integrals.
The integrals you describe are remarkably similar to a large variety of solutions we employ for area estimation and integration in general.
And then once you have the intersections, you only have to compute some internal polygons and then calculate some integrals.
Of course, probabilistic reasoning has similar computational problems, especially related to numerical evaluation of integrals in the denominator of Bayes' Rule.
Some universities skip the basics (set theory) and teach only the practical concepts (integrals).
Linear algebra & discrete math pop up a lot more than integrals in CS.
I've thought it was paradoxical that infinitely long curves could have finite integrals ever since I first took calculus.
It's an interesting hobby, like crocheting, writing poetry, or solving tricky integrals.
It's a Monte Carlo integration algorithm for solving the nasty integrals.
If one has any interest in quantum field theory, I would add complex analysis (countour integrals in particular) to that list.
Again, this integrals can be calculated using standard methods like Runge-Kutta.
Quote examples
For example, I refer you to the paper wherein some biologists "discovered" integrals in 1993.
Anyway, I already outlined the argument in another of my comments, where I talk about set theory and integrals - the "axiomatic" primitives are different bunch than "useful" primitives.
It is significantly more of a pain to roll your own pmvnorm, because you are now talking about efficient computation of high dimensional integrals, which always seems to involve a trip to Numerical Recipes or the like (see the Genz and Miwa references when you do "?pmvnorm" in R).
I remember our professor in introductory quantum mechanics saying something along the lines of: "and now you see why quantum mechanics is just Markov chains in imaginary time", but until another professor showed us the Wick rotation in the context of path integrals nobody really appreciated that even if it could have been in our grasp earlier.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use integrals in a sentence?
In quantum field theory you frequently do integrals in 4-ϵ as a way of regularizing divergent integrals.
What does integrals mean?
(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
What part of speech is integrals?
integrals is commonly used as noun.