Limit of sums | Integration or limit | Definite Integral | SAJAG JAIN | JAIN SIR

The development of the definition of the definite integral begins with a function, which is continuous on a closed interval. The given interval is partitioned into “ n” sub intervals that, although not necessary, can be taken to be of equal lengths. An arbitrary domain value, xi, is chosen in each sub interval, and its subsequent function value, is determined. The product of each function value times the corresponding sub interval length is determined, and these “ n” products are added to determine their sum. This sum is referred to as a Riemann sum and may be positive, negative, or zero, depending upon the behavior of the function on the closed interval.
The definite integral of any function can be expressed as the limit of a sum. Let us discuss definite integrals as a limit of a sum.
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