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.

• 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