In mathematics, the Burkill integral is an integral introduced by Burkill (1924a, 1924b) for calculating areas. It is a special case of the Kolmogorov integral.

References

Burkill, J. C. (1924a), "Functions of intervals", Proceedings of the London Mathematical Society, 22: 275–310, doi:10.1112/plms/s2-22.1.275, ISSN 0024-6115
Burkill, J. C. (1924b), "The expression of area as an integral", Proceedings of the London Mathematical Society, 22: 311–336, doi:10.1112/plms/s2-22.1.311
Skvortsov, V.A. (2001) [1994], "Burkill integral", Encyclopedia of Mathematics, EMS Press

v t e Integrals
Types of integrals	Riemann integral Lebesgue integral Burkill integral Bochner integral Daniell integral Darboux integral Henstock–Kurzweil integral Haar integral Hellinger integral Khinchin integral Kolmogorov integral Lebesgue–Stieltjes integral Pettis integral Pfeffer integral Riemann–Stieltjes integral Regulated integral
Integration techniques	Substitution Trigonometric Euler Weierstrass By parts Partial fractions Euler's formula Inverse functions Changing order Reduction formulas Parametric derivatives Differentiation under the integral sign Laplace transform Contour integration Laplace's method Numerical integration Simpson's rule Trapezoidal rule Risch algorithm
Improper integrals	Gaussian integral Dirichlet integral Fermi–Dirac integral complete incomplete Bose–Einstein integral Frullani integral Common integrals in quantum field theory
Stochastic integrals	Itô integral Russo–Vallois integral Stratonovich integral Skorokhod integral
Miscellaneous	Basel problem Euler–Maclaurin formula Gabriel's horn Integration Bee Proof that 22/7 exceeds π Volumes Washers Shells