Lesson 32: Applications of Integration: Surface Area
Preview
Lesson Preview
In this lesson we'll finish our calculus adventure -- in the sense of finishing the development of new calculus concepts and content -- by learning how to calculate the surface area of a surface of revolution. In Module 1 we'll derive the main formula by studying the simplest case of it: the area of the surface of the frustum of a right circular cone. (We'll see that the arc length content we learned in the previous lesson will pop up in a natural way.) Then, in Module 2 we'll work through examples of using the main formula. We'll see in one case that we'll need to draw on some of the integration techniques we've discussed in the course.
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
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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.
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