Substitution Rule

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

• Section 5.5 – The Substitution Rule

Expected Educational Results

• Objective 02–01: I can use a substitution to evaluate an indefinite integral.

• Objective 02–02: I can use a substitution to evaluate a definite integral using FTC-II.

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.

Substitution Rule

Definition: Substitution Rule for Indefinite Integrals

If $u=g(x)$$u=g(x)$ is a differentiable function, then

$\int f(g(x))g^{\prime }(x)dx=\int f(u)du$$\int{f\left(g(x)\right)g^{\,\prime}(x)\,dx}=\int{f(u)\,du}$

Investigation 01

1. What do you notice about the integrand on the left side of the equation in the definition above? Explain.

2. What do you notice about the integrand on the right side of the equation in the definition above? Explain.

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Last Modified: Monday, 9 August 2021 15:56 EDT