Lesson Plan: Area between Curves Mathematics • Higher Education

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to apply integration to find the area bounded by the curves of two or more functions.

Objectives

Students will be able to

  • use definite integrals to find the area between a curve and a nonhorizontal or vertical line,
  • use definite integrals to find the area between the curves of two given functions 𝑦=𝑓(𝑥) and 𝑦=𝑔(𝑥),
  • use definite integrals to find the area between the curves of two given functions 𝑥=𝑓(𝑦) and 𝑥=𝑔(𝑦),
  • use definite integrals to find the area of a region bounded by more than two curves (and/or lines),
  • use definite integrals to find the area of a compound region between two curves where the integral must be broken into two subintegrals.

Prerequisites

Students should already be familiar with

  • definite integrals,
  • finding the area between a curve and a vertical or horizontal line.

Exclusions

Students will not cover

  • improper integrals.

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