Geodesic
An estimate of the mean remainder term in quadrature formulae
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 1 (1961) no. 1, pp. 64-77

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The author finds the mathematical expectation of the error in numerical quadrature for a certain class of function (those whose first p derivatives are bounded and whose pth derivatives satisfy the Hцlder condition with index $\lambda$). Both one-dimensional and multi-dimensional integrals are considered. 
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     title = {An estimate of the mean remainder term in quadrature formulae},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {1},
     year = {1961},
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N. S. Bakhvalov. An estimate of the mean remainder term in quadrature formulae. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 1 (1961) no. 1, pp. 64-77. http://geodesic.mathdoc.fr/item/ZVMMF_1961_1_1_a2/