Lesson 18: Integration Properties and Rules

Preview

Here's the on-ramp for this lesson.


What Will We Learn?

  • This lesson focuses on studying the properties of integration (i.e., is the integral of a sum of functions the sum of their integrals?) and on starting a discussion of integration rules. We will also learn about "net signed area," which describes how one can still interpret negative values of definite integrals in terms of areas.


Why Do We Need to Learn This?

  • In the previous lesson we learned the theory behind calculating definite integrals. This lesson furnishes the practical aspects of that. By starting our study of integration rules and techniques we will start building up a table of integrals similar to our table of derivatives -- both handy references for calculating integrals (and derivatives). (The inner flaps of Calculus Simplified summarize some of the simplest integral rules and results.)

Review

Learn

The lesson notes below contain a learning plan with three stages -- Learn, Reflect, and Practice -- and guidance for what to do within each stage. Some tips for you as you work through this resource, and those that it points to:

  • I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.

Lesson Notes

Lesson 18.pdf

Video 1 (Examples 5.9-5.12)

Video 2 (Examples 5.13-5.14)

Video 3 (Example 5.15)

Reflect

If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:

  • Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.

  • Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.

If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:

  • Please summarize the main mathematical takeaways from the lesson notes.

  • What was the most interesting part of what you learned, and why?

  • What, if anything, do you still find confusing?

Practice

Work through the practice problems suggested below to see how much of this lesson you've understood.

Lesson 18 PP.pdf