Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Antiderivatives and Slope Fields

9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

TI Connect™

• ##### Accessories

TI Connectivity Cable

## Above and Beyond

#### Activity Overview

In this Computer Algebra System (CAS) activity, students create a general solution for calculating the ratio of the areas above and below a curve.

#### Before the Activity

• Install TI Connect™ using the TI connectivity cable
• See the attached PDF file for detailed instructions for this activity
• Print pages 1 - 2 from the attached PDF file for the class
• #### During the Activity

Distribute the pages to the class.

• Plot the lines y = x, y = 1, and x = 1
• Form a square using segments on the lines y = 1 and x = 1
• Evaluate the ratio of the area of the triangle above the y = x line to the area of the triangle below the y = x line
• Notice that the ratio is 1 : 1

• Plot the curves y = x2, y = 1, and x = 1
• Evaluate the areas above and below the curve by integrating them numerically
• Note that the ratio of the areas is 2 : 1

• Understand that if the index of x in the curve is n, then the ratio of the areas of the curves will be n : 1
• Realize that if the index of x is a negative integer, there is no area enclosed under the graph in the specified interval
• Repeat the problem with different values of n over various intervals

• Use CAS to explore the two areas
• #### After the Activity

Students' answer questions on the Activity sheet.

Review student results:

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