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An integral expressed as the difference between the values of the integral at specified upper and lower limits of the independent variable.

*‘He attended courses by Dirichlet on the theory of numbers, on potential theory, on definite integrals, and on partial differential equations.’**‘In Abel's third paper, Solutions of some problems by means of definite integrals he gave the first solution of an integral equation.’**‘His doctoral dissertation On definite integrals and functions with application in expansion of series was an early investigation of the theory of singular integral equations.’**‘His mathematical output remained strong and in 1814 he published the memoir on definite integrals that later became the basis of his theory of complex functions.’**‘His first paper on definite integrals appeared in the Messenger of mathematics.’*

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