How to Use The Washer Method To Calculate Volume (Calculus 2 Lesson 3)

In this video we look at how to use definite integrals to calculate the volume of solids of revolution that have holes by using the washer method. We discuss how to use the method when a region is revolved around the x-axis to form a solid, when a region is revolved around the y-axis to form a solid, and when the region is revolved around a line other than the x- or y-axis to form a solid. Additionally, we discuss the similarities between the disk and washer method.

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This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!


Video Chapters:
0:00 The Washer Method (x-axis)
6:40 The Washer Method (y-axis)
8:40 Summary of Formulas & Comparison to Disk Method
10:26 Example 1 - y=x, y=x^2 around x-axis
17:07 Example 2 - y=x^2, x=1, y=0 around y-axis
24:13 How to Adjust Each Radius When Revolving Around Other Lines
27:15 Example 3 Part 1 - y=x, y=sqrt(x) around y=1
33:06 Example 3 Part 2 - y=x, y=sqrt(x) around y=-1
35:40 Example 3 Part 3 - y=x, y=sqrt(x) around x=1
38:43 Example 3 Part 4 - y=x, y=sqrt(x) around x=-1
41:28 Note About Disk Method
41:57 Outro


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