Area Between Curves

Author: John J Weber III, PhD Corresponding Textbook Sections:

Expected Educational Results

Bloom’s Taxonomy

A modern version of Bloom’s Taxonomy is included here to recognize various different levels of understanding and to encourage you to work towards higher-order understanding (those at the top of the pyramid). All Objectives, Investigations, Activities, etc. are color-coded with the level of understanding.

Bloom’s Taxonomy for different levels of understanding
Figure 1.1: Bloom's Taxonomy

Area Between Curves

Investigation 03

Use the embedded DESMOS graph below:

  1. Explain why the area between y=x3x+2 and y=3x+2 must Area >0.

  2. Solve the equation for x: x3x+2=3x+2.

    1. Explain why there must be three (3) solutions to the above equation.
    2. Compare the solutions to the above equation to the x-coordinates of the intersections of y=x3x+2 and y=3x+2. What do you notice? Explain.
  3. Explain why 22(x3x+2(3x+2))dx does not represent the area between y=x3x+2 and y=3x+2.

  4. Compare 20(x3x+2(3x+2))dx+02(3x+2(x3x+2))dx with 22|x3x+2(3x+2)|dx.

  5. What do you notice? Explain.

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Last Modified: Thursday, 17 September 2020 2:48 EDT