# Approximating the area under a curve modules

## Overview

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?

## Ximera Module

Two young mathematicians discuss the idea of area.

# Introduction to sigma notation

## Ximera Module

We introduce sigma notation.

# Approximating area with rectangles

## Ximera Module

We introduce the basic idea of using rectangles to approximate the area under a curve.