The Washer Method | Calculus 2 Lesson 3 - JK Math

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
📝 Examples Video: • The Washer Method Exam...
⏩ Next Lesson: • The Shell Method | Cal...
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📺 Calculus 1 Playlist: • Calculus 1
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#calculus
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[@SgMaxii]

Holyyyyyyyyy. I don't understand why it only has 100 likes. It solved all my questions detailed explication and clear pictures. Thank you so much!

[@JKMath]

You're very welcome! Glad to help :)

[@changes777]

This is an amazing video that clarifies so much confusion I have had for the past few days. Definitely a life saver here!

[@JKMath]

Thanks for sharing this, glad to know the video was helpful! :)

[@Danielys777]

You did better at explaining the topic than my professor and for that I am grateful, because none of the videos reccomened by him made me understand the concept behind the Washer method topic. In fact,I will send him your channel, so that he can recommend you to future students that may find this topic confusing or difficult. Thank you and God bless!

[@JKMath]

You're very welcome! Glad the videos are helpful for you. And thank you for the kind feedback and for spreading the word. That is very much appreciated! :)

[@Markopa-gc5nd]

HOLY MOLY BRO, thanks u so much the only thing I needed here was the adjustment of radius since our professor didn't explain it that much as the only example he showed us was when the region is located below the axis of revolution.

[@JKMath]

Glad I could help! It can be frustrating when the radius adjustments are skipped in lessons on the washer method. It seems to be a common thing that is overlooked, so I made sure to highlight it in this video :)

[@user-yq5ij6oy9p]

Thank you so much Josh for creating these amazing videos!! I am so glad I found you early on in the semester as I'm taking Calc 2, you've been more helpful than my teacher and more helpful than the common channels people usually recommend for math help!

[@JKMath]

You're very welcome! Thanks for taking the time to let me know, I'm glad that the videos are helpful for you. If you ever have any questions, please don't hesitate to ask. And feel free to spread the word! :)

[@bobtivnan]

With rotating about lines other than the x or y axes, I teach it a little differently because students tend to forget the addition and subtraction rules for R(x) and r(x). Instead, I tell them to turn it into an equivalent solid of revolution problem so that it becomes rotation around the x or y axis (which they already learned). Just translate the R(x) and r(x) by the distance between the given axis and the x-axis (or y-axis). In your first example (part a), students would get a new R(x)= x-1 and r(x)=sqrt(x)-1. Since these are just the negative of the expressions in your example, squaring makes them equivalent to the integrand in your work. Anyway, it's a stylistic preference and neither approach is "better". I just find it easier to teach this way. Great job on the entire video!

[@Okxygenn]

THANK YOUUUUUUU, Best KZbin explanation

[@jhannashaneruiz2591]

Thank you very much..I now understand how to get the inner radius and outer radius

[@JKMath]

You're welcome! Glad to know the video was able to help you :)

[@brodyeskelsen4389]

Dude this video is soo helpful! You Rock!

[@Amy-lj9uu]

thank you so much for this amazing video, I love your explanation it's so easy to understand, deeply appreciate it!

[@JKMath]

You're very welcome! Glad to help :)

[@malekabbr]

These lessons of how to calculate the volume using disk method washer method etc.... I never understood these concepts but when I found you I felt like I became like the best person that can solve these thanks for doing these videos and also when I finish calc 2 I hope your playlist on calc 3 would be finished and after finishing calc 3 I hope you finish your playlist on abstract algebra so that if I don't understand a concept in college may be I would look for your videos Thanks keep the hard work you are the best. 😊😊

[@JKMath]

Awesome! Glad to know these videos have been able to help you and give you confidence in solving these types of problems. I will return to working on finishing my Calculus 3 playlist this summer, so there is a chance I'll have it done in time for when you take the course. We'll see! :)

[@malekabbr]

@@JKMath oh, take your time on making the calc 3 videos cause calc 2 is so hard so it would take me a lot to finish it but because in college there are some concepts that I can't understand them so that's why I wanted you to make your calc 3 playlist done but for now just take your time. :)

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underated indeed!!!

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Thank you very much❤

[@user-cy6rh5cs4j]

you made it easy !

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THANK YOU

[@JKMath]

You’re welcome!

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