upper integral

upper integral

[′əp·ər ′int·ə·grəl] (mathematics) The upper Riemann integral for a real-valued function ƒ(x) on an interval is computed to be the infimum of all finite sums over all partitions of the interval, the sums having terms given by (xi -xi-1) yi , where the xi are from a partition, and yi is the largest value of ƒ(x) over the interval from xi-1to xi .