Properties of Midpoint Riemann Sums

In a midpoint Riemann sum, the function is evaluated at the left endpoint of each subinterval.

The midpoint of a subinterval is calculated as $\frac{a_i + a_{i+1}}{2}$.

Using the function value at the midpoint can reduce error when the function behaves approximately linearly over the subinterval.

Midpoint Riemann sums often yield a more accurate approximation than left or right Riemann sums.