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Preview
Preview
Here's the on-ramp for this lesson.
What Will We Learn?
In this lesson we'll discuss what is perhaps the most important theorem in calculus: the Fundamental Theorem of Calculus. This theorem not only connects differentiation and integration together -- and, specifically, shows us that these operations undo each other -- it also helps us calculate definite integrals. The version of the theorem that does that is sometimes referred to as the Evaluation Theorem (this is also how Calculus Simplified refers to it). Toward the end of the lesson we will start using the Evaluation Theorem to calculate simple definite integrals.
Why Do We Need to Learn This?
The Fundamental Theorem of Calculus, and the Evaluation Theorem, are two of the most widely used results in calculus (and in any discipline that uses calculus). They help us calculate integrals, relate differentiation problems to integration problems, and provide the foundation for later extensions of the results that apply in more advanced contexts (e.g., to calculus in three dimensions).
Review
Review
Learn
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 Notes
Lesson 17.pdfVideo 1 (Examples 5.3-5.4)
Video 1 (Examples 5.3-5.4)
Video 2 (Example 5.6)
Video 2 (Example 5.6)
Video 3 (Examples 5.7-5.8 )
Video 3 (Examples 5.7-5.8 )
Reflect
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
Practice
Work through the practice problems suggested below to see how much of this lesson you've understood.
Lesson 17 PP.pdfPage updated
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