Lesson 19: Review of Calculus 1 Integration

Preview

Unit Preview

  • This lesson marks the start of Unit 5: Integration -- Techniques of Integration. The lessons in this unit focus on building a repository of integration techniques that help us evaluate definite integrals. We'll start off simple by reviewing the basics of integration from Calculus 1 and also u-substitution. After that, we'll learn new integration techniques (not covered in a typical Calculus 1 course). At the end of this unit we'll be ready to tackle the last driving question in the course (How can we calculate the volume enclosed by a surface?), which we'll get to in the next unit.


Lesson Preview

  • In this lesson we'll review the basics of integration from Calculus 1. This includes the important notions of indefinite integrals and antiderivatives, the Evaluation Theorem, the Fundamental Theorem of Calculus, and the fact that the definite integral measures the "net signed area" between the graph of the function and the x-axis.

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 19.pdf

The videos below were recorded by me for the Calculus 1 course on this site. The example numbers below refer to examples in my book, Calculus Simplified.

Video 1 (Examples 5.3-5.4)

Video 2 (Example 5.6)

Video 3 (Examples 5.7-5.8)

Video 4 (Example 5.9-512)

Video 5 (Examples 5.13-5.14)

Video 6 (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 19 PP.pdf