Author:
Jim Fowler
Subject:
Calculus
Material Type:
Module
Level:
Community College / Lower Division, College / Upper Division
Provider:
Ohio Open Ed Collaborative
Tags:
  • Approximation
  • Curves
  • License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    eBook, Interactive

    Education Standards

    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

    Approximating area with rectangles

    Ximera Module

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