Approximating the area under a curve modules
After completing this section, students should be able to do the following.
- Express the sum of n terms using sigma notation.
- Apply the properties of sums when working with sums in sigma notation.
- Understand the relationship between area under a curve and sums of areas of rectangles.
- Approximate area of the region under a curve.
- Compute left, right, and midpoint Riemann sums with 10 or fewer rectangles.
- Understand how Riemann sums with n rectangles are computed and how the exact value of the area is obtained by taking the limit as n→∞n→∞ .
What is area?
Two young mathematicians discuss the idea of area.
Introduction to sigma notation
We introduce sigma notation.
Approximating area with rectangles
We introduce the basic idea of using rectangles to approximate the area under a curve.