The RiemannSum(f(x), x = a..b, method = midpoint, opts) command calculates the midpoint Riemann sum of f(x) from a to b. The first two arguments (function expression and range) can be replaced by a definite integral.

If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

Given a partition  of the interval , the midpoint Riemann sum is defined as:

where the chosen point of each subinterval  of the partition is the midpoint .

By default, the interval is divided into  equal-sized subintervals.

For the options opts, see the RiemannSum help page.

This integration method can be applied interactively, through the ApproximateInt Tutor.

Left Riemann Sum

Lower Riemann Sum

Right Riemann Sum

Upper Riemann Sum