Lesson 4: 5.5 The Substitution Rule
Duration of Days: 3
Lesson Objective
Students will be able to recognize specific types of integrals for which substitution can be used, and apply the substitution rule to solve those integrals.
- What must be included in an integral in order for us to use the substitution method to solve?
- How is the Chain Rule related to the Substitution Rule?
- Substitution Rule
- symmetric functions
(using substitution to solve integrals)
Recognize functions for which the substitution technique can be applied and then apply it correctly.
DOK levels 1-4
- calculation of total revenue or cost over time
- probabilities in statistics for continuous random variables
- population growth, radioactive decay
- filtering and analyzing data signals in electronics
- calculation of exact volumes or surface areas of irregular shapes
Students struggle at first with determining which part to substitute for and what will become part of "du".
Students also have difficulty with switching the limits of integration when switching the integral from being in terms of x to being in terms of u.
homogeneous grouping and whole-class discussion
section assessment
problems assigned from book