Activity Detail
If you are using a TI-73, TI-83, TI-84 or TI-89, there may be particular math or science applications you will need to download to use certain activities. If you are using TI-Nspire technology, please update your TI-Nspire handheld operating system or computer software to view the latest activities. The latest TI-Nspire operating system was released in June 2009.
Browse by Subject Submit Activity Saved Activities Advanced Search
  


add to saved activities



print this activity
 
Riemann Sums and the Fundamental Theorem of Calculus
 


Activity Overview

In this activity, students learn and explore how Indefinite integrals are used to find the antiderivative of a function. They also learn that Definite integrals can be used to find the area bounded by a function and the X-axis. From examples they learn that both types of integration can be connected together by the Fundamental Theorem of Integral Calculus.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 39 - 48 from the attached PDF file for your class

    		•

    		During the Activity

    		Distribute the pages to the class.

    Follow the Activity procedures:
    The Area Under a Parabola:
    Numerical Method:
  • Enter the function and graph it
  • Enter boundaries and number of rectangles
  • Use left-hand, right- hand, and midpoint Riemann Sums, and approximate the area bounded by the function


    • Analytical Method:
  • Define functions for the left-hand, right-hand, and midpoint rectangle methods
  • Evaluate the functions
  • Take the limit of each summation function as the number of rectangles approaches infinity
  • Find both approximate and exact values of the function for the area under the curve for the function
  • Notice that the area function is the antiderivative of f(x)
  • Find the area from a to b and predict the definite integral of the function with a and b as boundaries


    • Area Under other Curves:
  • Enter the function and find limits of the right-hand Riemann Sum to find the area from a to b
  • Compare the results with a corresponding definite integral
  • Notice that the limit of Riemann Sum is related to the antiderivative of the function

    		After the Activity

    		Students will complete the practice exercise problems.

    Review student results:
  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary

    		Other Downloads




    view standards alignment
    view textbook alignment

    Subject Area:
    Math : Calculus : Integrals, Antiderivatives and Indefinite Integrals

    Author:
    Texas Instruments

    Level:
    9-12

    Activity Time:
    60 Minutes

    Device:
    TI-89 / TI-89 Titanium

    Apps:
     

    Software:
     

    Accessories:
     

    Other:
    This is Activity 5 from the EXPLORATIONS Book:
    Advanced Placement Calculus with the TI-89.

    Report an issue with this activity