Computation of definite integral over repeated integral

Abstract

The tasks involving repeated integral occur from time to time in technical practice. This paper introduces the investigation of the authors in the eld of repeated integrals within the required class of functions. Denite integral over repeated integral is focused
and a tool for its computation is developed. The solving tool involves two principal steps, analytical and numerical one.
In the analytical step the denite integral over a repeated integral is decomposed to n integrals and thereafter the Cauchy form is used for further rearrangement. Numerical step involves Gauss type integration slightly modied by authors. Several examples
illustrating the functioning of both analytical and numerical steps of the method are provided along the paper.