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 01

Use the embedded DESMOS graph below:

  1. Identify the shaded region representing the area under f(x)=sin(πx) on [0,0.5].
  2. Identify 00.5sin(πx)dx.
  3. Identify the shaded region representing the area under g(x)=2x on [0,0.5].
  4. Identify 00.52xdx.
  5. Identify the shaded region representing the area \textbf{between} f(x)=sin(πx) and g(x)=2x on [0,0.5].
  6. Compare 00.5sin(πx)dx00.52xdx with 00.5(sin(πx)2x)dx.
  7. What do you notice? Explain.

CC BY-NC-SA 4.0

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

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