Lesson: Riemann Sums Mathematics • 12th Grade

In this lesson, we will learn how to approximate the area under the curve of a function using right, left, and midpoint Riemann sums.

Lesson Plan

Students will be able to

use rectangles to approximate areas under curves,
understand the difference between right, left, and midpoint Riemann sums,
recognize the circumstances under which right or left Riemann sums underestimate or overestimate the area under a curve.

Lesson Video

Lesson Worksheet

Q1:

Given that and that , evaluate, to the nearest six decimal places, the Riemann sum for with six subintervals, taking the sample points to be left endpoints.

Q2:

Let over . Using four subintervals and taking midpoints as sample points, evaluate the Riemann sum of to six decimal places.

Q3:

Given and , evaluate the Riemann sum for with six subintervals, taking sample points to be midpoints.