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Integral

In mathematics, an integral is the continuous analog of a sum, and is used to calculate areas, volumes, and their generalizations. The process of computing an integral, called integration, is one of the two fundamental operations of calculus, along with differentiation. Integration was initially used to solve problems in mathematics and physics, such as…

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Overview

History

Terminology and notation

Formal definitions

Properties

Fundamental theorem of calculus

Extensions

Applications

Computation

Online books

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Integral

Nodes255
Edges254
Triples265
Avg. degree1.99
Density0.007843
Components1

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Integral

Top relations

related to Online books · 39
Integral → An Approach Using Infinitesimals, Benjamin, Brief Introduction, Calculus, CIT, Dan, Definite Integrals, Difference Equations, Differential Equations Archived, Elementary Calculus, Elementary Treatise, Evaluation, Faraz, First-Year CalculusHussain, Fullerton College, HathiTrust, Holistic Numerical Methods InstituteP, Infinitesimal Calculus, Integral Calculus, Integration
related to Other integrals · 31
Integral → Aleksandr Khinchin, Alfréd Haar, Although, Arnaud Denjoy, Banach, Brownian, Darboux, Darboux-integrable, Gustave Choquet, Jaroslav Kurzweil, Johann Radon, Kurzweil, Lebesgue, Oskar Perron, Ralph Henstock, Riemann, Riemann-integrable, Stieltjes, Stratonovich, The
related to Inequalities · 24
Integral → An, Cauchy, Daniell, For, Hilbert, Hölder's, If, In, Inequalities, Lebesgue, Lp, Minkowski, Moreover, Products, Riemann-integrable, Schwarz, Since, Subintervals, Suppose, That
related to Formalization · 15
Integral → Although, Bishop Berkeley, Calculus, Fourier, Integration, Lebesgue, Lebesgue's, Leibniz, Newton, Other, Riemann, Riemann's, Riemann-integrable, These, While Newton
related to Numerical · 13
Integral → Chebyshev, Clenshaw, Cotes, Curtis, Definite, Higher, Newton, One, Riemann, Runge's, Simpson's, The, This
related to Pre-calculus integration · 13
Integral → AD, Archimedes, BC, China, Chinese, Democritus, Eudoxus, Greek, Liu Hui, The, This, Zu Chongzhi, Zu Geng
related to Lebesgue integral · 11
Integral → For, However, It, Lebesgue, Paul Montel, Riemann, Riemann-integrable, Such, Then, Therefore, Thus Henri Lebesgue
related to Symbolic · 10
Integral → Extensive, However, Macsyma, Many, Maple, Mathematica, On, Symbolic, The Risch, With
related to Historical notation · 8
Integral → French Academy, Gottfried Wilhelm Leibniz, He, Isaac Newton, Joseph Fourier, Latin, Mémoires, The
related to Analytical · 7
Integral → Let, Most, Provided, Sometimes, Techniques, The, Then

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Important terminology

function integration integrals functions interval riemann calculus area lebesgue one used sum defined displaystyle differential surface values may volume also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Integralis acontinuous analog of a sum0.90text
Integralis aLebesgue integral0.90text
Integralis aelement of V0.90text
Integralis alimit as that endpoint goes to infinity0.90text
Integralis asum of values of the field at all points on the curve0.90text
Integralis asum of the field at all points on the surface0.90text
Brownian motion.The Young integralinstance ofwhich define integration with respect to semimartingales0.80text
which is a kind of Riemanninstance ofwhich define integration with respect to semimartingales0.80text
an electric field or gravitational fieldinstance ofFor an object moving along a path C in a vector field F0.80text
the total work done by the field on the object is obtained by summing up the differential work done in moving from s to sinstance ofFor an object moving along a path C in a vector field F0.80text
water or airinstance ofThe fluid flux in this example may be from a physical fluid0.80text
or from electrical or magnetic fluxinstance ofThe fluid flux in this example may be from a physical fluid0.80text

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