5.2 Integration & Anti-derivatives
Question #1 (Easy): Riemann Sum Using the Midpoints
Riemann sum using the midpoints as sample points are calculated as: ∑ ̅ , where the
midpoint for each subinterval is determined by ̅ .
Riemann sum represents the sum of all the rectangles under the curve.
Midpoints always present the best estimate. For increasing functions, left endpoints are associated with
the lower estimate, and the right endpoints the upper estimate. Likewise, for decreasing functions, vice
versa, meaning the left endpoints give the upper estimate and the right endpoints the upper estimate.
1) Find the Riemann sum for , with . Take the midpoints as the
2) What does the Riemann sum represent?