Riemann integral

Basic integral in elementary calculus

In real analysis, the Riemann integral is a rigorous definition of the integral of a function on an interval. It defines the integral by approximating the region under the graph of a function by finite sums of areas of vertical rectangles. For suitable functions, including every continuous function on a closed bounded interval, these Riemann sums approach a single limiting value as the partitions of the interval become finer.

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