AP Calculus AB and BC glossary
Midpoint Riemann sum
A midpoint Riemann sum uses the height of the function at the centre of each subinterval. It is normally far more accurate than a left or right sum, and where concavity does not change it errs in the opposite direction to the trapezoidal rule.
On an interval of unchanging concavity the midpoint rule underestimates where the graph is concave up and the trapezoidal rule overestimates, so the true value lies between them.
The mistake
Reading midpoints off a data table that does not contain them. A midpoint sum needs the function value at the centre, which a table of endpoints usually will not give you.
Appears in: Unit 6: Integration and Accumulation