integer Whole-valued positive or negative number or 0. The integers are generated from the set of counting numbers 1, 2, 3,... and the opera¬ tion of subtraction. When a counting number is subtracted from itself, the result is zero. When a larger number is subtracted from a smaller num¬ ber, the result is a negative whole number. In this way, every integer can be derived from the counting numbers, resulting in a set of numbers closed under the operation of subtraction (see group theory).
integral Fundamental concept of calculus related to areas and other quantities modeled by functions. A definite integral gives the area between the graph of a function and the horizontal axis between vertical lines at the endpoints of an interval. It also calculates the net change in a system over an interval, thus leading to formulas for the work done by a varying force or the distance traveled by an object moving at varying speeds. When only the function is given, with no interval, it is known as an indefinite integral. The process of solving either a definite or an indefi¬ nite integral is called integration. According to the fundamental theorem of calculus, a definite integral can be calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). Integrals extend to higher dimensions through multiple inte¬ grals. See also line integral; surface integral.
integral, line See line integral integral, surface See surface integral
integral calculus Branch of calculus concerned with the theory and applications of integrals. While differential calculus focuses on rates of change, such as slopes of tangent lines and velocities, integral calculus deals with total size or value, such as lengths, areas, and volumes. The two branches are connected by the fundamental theorem of calculus, which shows how a definite integral is calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). For example, integrating a velocity function yields a distance function, which enables the distance traveled by an object over an inter¬ val of time to be calculated. As a result, much of integral calculus deals with the derivation of formulas for finding antiderivatives. The great util¬ ity of the subject emanates from its use in solving differential equations.
integral equation In mathematics, an equation with an unknown function within an integral. An example is
f(x) = | cos (xf)(p(t)dt
where f[x) is known and cp(r) is to be found, given certain conditions on /. Such equations are useful in solving differential equations.
integral transform In mathematics, a function that results when a given function is multiplied by a so-called kernel function, and the product is integrated (see integration) between suitable limits. Its value lies in its ability to simplify intractable differential equations (subject to particular
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946 I integrated circuit ► intention
boundary conditions) by transforming the derivatives and boundary condi¬ tions into terms of an algebraic equation that may easily be solved. The solu¬ tion yielded must be converted to the final solution using an inverse transformation. Several integral transforms are named for the mathemati¬ cians who introduced them (Fourier transform, Laplace transform).
integrated circuit (1C) or microcircuit or chip or microchip
Assembly of microscopic electronic components (transistors, diodes, capacitors, and resistors) and their interconnections fabricated as a single unit on a wafer of semiconducting material, especially silicon. Early ICs of the late 1950s consisted of about 10 components on a chip 0.12 in. (3 mm) square. Very large-scale integration (VLSI) vastly increased circuit density, giving rise to the microprocessor. The first commercially success¬ ful IC chip (Intel, 1974) had 4,800 transistors; Intel’s Pentium (1993) had 3.2 million, and more than a billion are now achievable.
integrated pest management Technique for agricultural disease- and PEST-control in which as many pest-control methods as possible are used in an ecologically harmonious manner to keep infestation within manageable limits. Integrated pest management addresses the serious eco¬ logical problems created by the extensive use of powerful chemical pes¬ ticides. It minimizes their use and combines them with biological methods of pest control, including the breeding of pest-resistant crop varieties, the development of crop culture methods that inhibit pest proliferation, the release of predators or parasites of the pest species, and the placement of traps baited with the pest’s own sex attractants (pheromones). Chemical insecticides generally are applied only as a last resort.
Integrated Services Digital Network See ISDN
integration In calculus, the process of finding a function whose deriva¬ tive is a given function. The term, sometimes used interchangeably with “antidifferentiation,” is indicated symbolically with the integral sign J. (The differential dx usually follows to indicate x as the variable.) The basic rules of integration are: (1) j(f + g)dx = \fdx + \gdx (where/and g are functions of the variable x), (2) J kfdx = k)fdx (k is a constant), and (3)
(C is a constant). Note that any constant value may be added onto an indefinite integral without changing its derivative. Thus, the indefinite integral of 2x is x + C, where C can be any real number. A definite inte¬ gral is an indefinite integral evaluated over an interval. The result is not affected by the choice for the value of C. See also differentiation.
integument Un-'teg-yu-monA Covering of the body, which protects it from the outside world and from drying out. In humans and other mam¬ mals it consists of the skin (including outer epidermis and inner dermis) and its related structures, including hair, nails, and sebaceous and sweat glands.
Intel Corp. U.S. manufacturer of semiconductor computer circuits. Intel was founded in 1968 as NM Electronics by Robert Noyce and Gordon Moore, inventors of the integrated circuit, to manufacture large-scale inte¬ grated (LSI) circuits. In the early 1970s it introduced the most powerful semiconductor chips then known, which soon replaced the magnetic cores previously used in computer memories. IBM chose to use Intel’s 8088 microprocessor (introduced 1978) in its first personal computer (the IBM PC), and Intel microprocessors became standard for all PC-type machines. Although other manufacturers eventually developed Intel-compatible microprocessors, Intel continued to power more than 75% of PCs at the beginning of the 21st century.
intellectual property Property that derives from the work of an indi¬ vidual’s mind or intellect. Early copyright law aimed to protect the eco¬ nomic interests of book publishers rather than the intellectual rights of authors. Modem copyright law protects the labour of elaborating an idea, but not the idea itself. The concept of discovery also plays a role in intel¬ lectual property rights: a patent is awarded to one who can demonstrate that he or she has invented something not previously known. The World Trade Organization requires members to establish and enforce minimum levels of copyright, patent, and trademark protection within their jurisdic¬ tions. The World Intellectual Property Organization, which began opera¬ tions in 1970, promotes the worldwide protection of both industrial property (inventions, trademarks, and designs) and copyrighted materials (literary, musical, photographic, and other artistic works).
intelligence In education, the ability to leam or understand or to deal with new or challenging situations. In psychology, the term may more specifically denote the ability to apply knowledge to manipulate one’s environment or to think abstractly as measured by objective criteria (such as the IQ test). Intelligence is usually thought of as deriving from a com¬ bination of inherited characteristics and environmental (developmental and social) factors. The subject remains hotly debated, and many have tried to show that either biology (especially genes) or environment (espe¬ cially conditions reflecting socioeconomic class) are more or less exclu¬ sively responsible for producing differences in intelligence. Particularly contested have been studies purporting to show links between ethnic heri¬ tage and intelligence, most of which have not been accepted in the sci¬ entific community. General intelligence is often said to comprise various specific abilities (verbal ability, ability to apply logic in solving problems, etc.), but critics contend that such compartments fail to reflect the nature of cognition and that other models, perhaps based on information process¬ ing, are needed. High intelligence (as measured by tests) is sometimes shown to correlate with social achievement, but most experts believe other factors are important and that intelligence is no guarantor of success (and its lack is no guarantor of failure). See also artificial intelligence; creativity.