Finite Sums, Limits, and Definite Integrals
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To calculate a Riemann Sum, you need a function, an interval, and a partition. The number of subintervals in the partition is denoted by n. The length of the longest subinterval is called the norm of the partition. If each subinterval is equal in length, it is called a regular partition.
If the number of subintervals, n, in a regular partition approaches infinity, the norm of the partition approaches zero. Although a Riemann Sum can be calculated by evaluating the function at any value from each subinterval, in practice we generally choose the left endpoint, right endpoint, or midpoint. These are called LRAM, RRAM, MRAM and can be denoted