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 02

Use the embedded DESMOS graph below:

  1. Explain why Area 0.

  2. Identify the shaded region representing the area between x=y2 and the y-axis on 1y2].

  3. Identify the shaded region representing the area under x=y24 on 1y2].

  4. Which of the two shaded regions above is the larger shaded region? Explain.

  5. Identify the shaded region representing the area \textbf{between} x=y2 and x=y24 on 1y2].

  6. Solve the equation for y: y2=y24

    1. Explain why there must be two solutions to the above equation.
    2. Compare the solutions to the above equation to the y-coordinates of the intersections of x=y2 and x=y24. What do you notice? Explain.
  7. Identify 12(y2)dy.

  8. Identify 12(y24)dx.

  9. Which of the above two integrals is the larger value? Explain.

  10. Compare 12(y2)dx12(y24)dx with 12(y2(y24))dx.

  11. What do you notice? Explain.

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