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.
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