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Lesson Plan: Integrating Standard Functions Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to integrate standard functions including polynomial, trigonometric, and exponential functions and use the reverse chain rule to integrate functions of the form 𝑓(𝑎𝑥+𝑏).

Objectives

Students will be able to

  • solve indefinite integrals where the integrand is
    • a power function,
    • an exponential function,
    • a reciprocal function,
    • sin𝑥, cos𝑥, or sec𝑥,
    • coseccot𝑥𝑥, cosec𝑥, or sectan𝑥𝑥,
  • find indefinite and definite integrals of the sums and differences of the above functions,
  • find the value of a constant in a definite integral, given the value of that integral,
  • integrate functions of the form 𝑓(𝑎𝑥+𝑏).

Prerequisites

Students should already be familiar with

  • indefinite and definite integrals of 𝑥,
  • differentiating power, exponential, logarithmic, trigonometric, and reciprocal trigonometric functions.

Exclusions

Students will not cover

  • integration using trigonometric identities,
  • integration by substitution.

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