Lesson Plan: Properties of Definite Integrals Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use properties of definite integration, such as the order of integration limits, zero-width limits, sums, and differences.
Objectives
Students will be able to
- understand the effect of reversing the limits of integration,
- understand how to add and subtract the limits of integration for adjacent intervals,
- understand the zero-width property of integration,
- understand how to manipulate integrals containing the sum (or difference) of two continuous functions,
- understand how to manipulate integrals that contain a constant multiple in the integrand,
- understand comparison properties of integrals, that is, how to compare integrals of two functions using a given relationship (i.e., ),
- understand the maximum and minimum inequality property of integrals,
- understand how to manipulate integrals of odd and even functions.
Prerequisites
Students should already be familiar with
- definite integrals.
Exclusions
Students will not cover
- indefinite integrals,
- differentiation.
