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

    Education Standards

    Definite integrals modules

    Overview

    After completing this section, students should be able to do the following.

    • Use integral notation for both antiderivatives and definite integrals.
    • Compute definite integrals using geometry.
    • Compute definite integrals using the properties of integrals.
    • Justify the properties of definite integrals using algebra or geometry.
    • Understand how Riemann sums are used to find exact area.
    • Define net area.
    • Approximate net area.
    • Split the area under a curve into several pieces to aid with calculations.
    • Use symmetry to calculate definite integrals.
    • Explain geometrically why symmetry of a function simplifies calculation of some definite integrals.

    Computing areas

    Ximera Module

    Two young mathematicians discuss cutting up areas.

    The definite integral