Multiple Integral

(redirected from Multiple integration)

multiple integral

[′məl·tə·pəl ′int·ə·grəl]
(mathematics)
An integral over a subset of n-dimensional space.

Multiple Integral

an integral of a function defined on some region in a plane and in three-dimensional or n -dimensional space. The corresponding multiple integrals are referred to as double integrals, triple integrals, and n-tuple integrals, respectively.

Let the function f(x, y ) be defined on some region D of the plane xOy. Let us divide D into n subregions di whose areas are equal to si, choose a point (ξi, ηi) in each subregion di (see Figure 1), and form the integral sum

If as the maximal diameter of the subregions d, decreases without bound the sums S have a limit independent of the choice of the points (ξi, ηi), then this limit is called the double integral of the function f(x, y) over the region D and is denoted by

∫ ∫Df (x,y) ds

A triple integral and, in general, an n -tuple integral are defined analogously.

Figure 1

In order for the double integral to exist, it is sufficient that, for example, the region D be a closed (Jordan) measurable region and that the function f(x, y) be continuous throughout D. Multiple integrals possess a number of properties similar to those of ordinary integrals. In order to calculate a multiple integral we reduce it to an iterated integral. Green’s formulas and the Green-Ostrogradskii theorem can be used in special cases to reduce multiple integrals to integrals of lower dimension. Multiple integrals find wide application. Volumes of bodies, as well as masses, static moments, and moments of inertia ( of bodies, for example) are expressed using multiple integrals.

References in periodicals archive ?
Mohamed Ebrahim, Product Planning at The Topps Company also remarked: "We turned to Snapfulfil, not only for their expertise in delivering Cloud WMS, but they also offered multiple integration routines to our eCommerce site and Oracle host system, allowing us to streamline our operation, lower IT costs and improve customer service.
The new RailTuff cable has a transmission performance of 10 Gbps, enabling multiple integration of board applications and effectively making cable installations future proof.
CAA had a tight timeline of 14 months to roll out the Guidewire enterprise system and Turack points out such a quick installation is difficult with multiple integration touch points, whether it is regulatory constraints or just internal adoptions from an integration perspective.
While it offers system manufacturers time-to-market advantage, it also enables simplified manufacturing process such that multiple integration steps that exist in today's system manufacturing can now be consolidated into one single step.
GTSI also offers multiple integration services and partners with globally recognized service providers to bring customers a wide selection of more complex integration options.
Survey results indicate the existence of multiple integration barriers, which include time and cost considerations, as well as a lack of supplier-centric solutions, resulting in a shortage of end-to-end integration in the market.
Through the gateway and the Clearent Developer Center, Clearent is able to offer developers both one-time and recurring payments, multiple integration options, access to complete working code samples and live support from payments professionals who know the industry and are there to ensure that clients can seamlessly integrate payments to their software program or application.
As a consequence, our customers are requesting that nJAMS supports multiple integration platforms for end-to-end process monitoring.
Those organizations focused on data integration were significantly more likely to have a single, integrated team that handles multiple integration disciplines.
The CRM system currently in use by the City includes multiple integration points with other City systems, including ESRI GIS, PeopleSoft CIS, Chameleon, InforEAM and CityWorks.
BlueSnap has reinvented and optimized the checkout experience by combining intelligent payment routing, frictionless one-click checkout, cross-border payments, award-winning Smart Subscriptions, multiple integration options and dynamic eCommerce tools.

Site: Follow: Share:
Open / Close