integral calculus


integral calculus
the branch of mathematics that deals with integrals, esp. the methods of ascertaining indefinite integrals and applying them to the solution of differential equations and the determining of areas, volumes, and lengths.
[1720-30]

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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 interval of time to be calculated. As a result, much of integral calculus deals with the derivation of formulas for finding antiderivatives. The great utility of the subject emanates from its use in solving differential equations.

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Universalium. 2010.

Look at other dictionaries:

  • Integral calculus — Integral In te*gral, a. [Cf. F. int[ e]gral. See {Integer}.] [1913 Webster] 1. Lacking nothing of completeness; complete; perfect; uninjured; whole; entire. [1913 Webster] A local motion keepeth bodies integral. Bacon. [1913 Webster] 2. Essential …   The Collaborative International Dictionary of English

  • Integral calculus — Calculus Cal cu*lus, n.; pl. {Calculi}. [L, calculus. See {Calculate}, and {Calcule}.] 1. (Med.) Any solid concretion, formed in any part of the body, but most frequent in the organs that act as reservoirs, and in the passages connected with… …   The Collaborative International Dictionary of English

  • integral calculus — ► NOUN Mathematics ▪ the part of calculus concerned with the integrals of functions …   English terms dictionary

  • integral calculus — n. the branch of higher mathematics that deals with integration and its use in finding volumes, areas, equations of curves, solutions of differential equations, etc …   English World dictionary

  • integral calculus — noun the part of calculus that deals with integration and its application in the solution of differential equations and in determining areas or volumes etc. • Topics: ↑mathematics, ↑math, ↑maths • Hypernyms: ↑calculus, ↑infinitesimal calculus * * …   Useful english dictionary

  • integral calculus — noun The calculus that generalizes summation to find areas, masses, volumes, sums, and totals of quantities described by continuously varying functions. See Also: integral, integration …   Wiktionary

  • integral calculus — noun Mathematics the part of calculus concerned with the integrals of functions …   English new terms dictionary

  • integral calculus — noun Date: circa 1741 a branch of mathematics concerned with the theory and applications (as in the determination of lengths, areas, and volumes and in the solution of differential equations) of integrals and integration …   New Collegiate Dictionary

  • integral calculus — branch of mathematics dealing with determining methods of calculating lengths areas and volumes …   English contemporary dictionary

  • integral calculus — noun (U) technical a method of measuring the distance a moving object has moved at a particular moment, by using your knowledge of its speed until then …   Longman dictionary of contemporary English


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