Multiple Integral

(redirected from Multiple integration)

multiple integral

[′məl·tə·pəl ′int·ə·grəl]
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 ?
This solution has multiple integration points into the hotel, including room controls, point-of-sale systems, property management systems, hotel service providers, hotel communications, social media posting sites, IPTV controls and third-party reservation systems.
Utilizing multiple integration points beyond connecting and normalizing data provides users with full visibility into their business and enables them to make smarter and faster business decisions.
We are offering competitive pricing and a full web-based portal with multiple integration options for easy operations that can be adopted by any organisation," added Kubaisi.
We are offering competitive pricing, and a full web-based portal with multiple integration options for easy operations that can be adopted by any organisation," added al-Kubaisi.
PID51 also lets each ply have multiple integration points in the thickness.
The topics are infinite series; parametric equations, polar coordinates, and conic sections; vector geometry; the calculus of vector-valued functions; differentiation in several variables; multiple integration; line and surface integrals; and fundamental theorems of vector analysis.
To address data growth, organizations are partnering with technology companies to invest in multiple integration strategies and technologies.
Multiple systems also mean multiple integration points to customer data and CRM systems.
During the Microsoft/Nokia integration, there were periods where Hawes oversaw multiple integration teams totalling up to 250 people, often "following the sun" as one team in China would hand off work to Helsinki, and then Helsinki would hand off a project to the Seattle headquarters.
The new RailTuff cable has a transmission performance of 10 Gbps, enabling multiple integration of board applications and effectively making cable installations future proof.
Assisting Textron Systems Canada and TM&LS in its program to manufacture, field and support the TAPV starting in 2014 are: Rheinmetall Canada, which is tasked with performing multiple integration functions, final assembly and service support; Kongsberg Protech Systems Canada, which is supplying a version of its Protector Dual Remote Weapon Station; and Engineering Office Diesenroth Canada (EODC), which is responsible for providing add-on armour components.
Why should an insurer invest in a single platform when multiple integration points with their preferred partners already exist?

Full browser ?