AP Calculus AB and BC glossary
Left Riemann sum
A left Riemann sum approximates a definite integral using the left endpoint of each subinterval as the rectangle height. For an increasing function every rectangle sits below the curve, so the sum underestimates the integral; for a decreasing function it overestimates.
The direction of the error depends on whether the function is increasing or decreasing, not on concavity. That is the opposite of the midpoint and trapezoidal rules, whose error direction depends on concavity instead.
The mistake
Using the wrong number of terms. With n subintervals a left sum uses the first n endpoints and skips the last one, so the final data point in a table is never used.
Appears in: Unit 6: Integration and Accumulation