Disk Washer Method to Find the Volume of Solids of Revolution | Calculus 2

In this video, you will learn to calculate the volume of three-dimensional solids using the disk or dish washer method and solids of revolution, specifically around the x-axis. We already learned how to find the area using integration in two-dimensional calculus, but we can also calculate the volume of three-dimensional objects or solids too!
So what exactly is a solid of revolution and dish washer method? Don't worry; it's not as scary as it sounds. If you have a function, and you revolve it around the x-axis or the y-axis, you will obtain a three-dimensional object or solid. Using definite integration, we can calculate the volume of this solid with calculus 2!
This video will give you plenty of examples and practice problems to help you calculate the volume of solids of revolution. We will deal with circular cross-sections and find the area of cross-sections which are circles.
In the next video, we will take a look at solids of revolution around ANY horizontal lines below the x-axis. The video after that will be about solids of revolution around ANY horizontal lines above the x-axis. Stay tuned!
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[@____Paul____]

You're contributing a lot to the world here, one clear explanation at a time! Thank you!!

[@QuocDatPhung]

Thank you for your kind words Paul!

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HIIIII THANK YOU SO MUCHH, IT'S REALLY HELPING THAT YOUR EXPRESSIONS IS NOT SCARY. IT WAS LIKE TLKING TO MY CLASSMATE VIA VIDEOCCAALLL TENKIESS

[@QuocDatPhung]

Haha thank you! Don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@Cactusszss]

I love this guy he has helped me so much thank you so much for making these videos your the reason I'm passing calc 2

[@QuocDatPhung]

I'm really happy to hear that!

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Thank you from Iraq ...you are very talented...

[@deborahmminele9902]

very much appreciate how you patiently guide us on how to go about this tricky section. You made my life easier and I will never be able to thank you enough🙏🙏

[@QuocDatPhung]

I'm so happy to hear that Deborah! Please kindly subscribe and share with your friends my Calculus playlist: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@ptyptypty3]

I've said it before and I WILL SAY IT AGAIN.... you are the BEST !!! your explanations and diagrams are PERFECT !! Keep up the great work!! you are smart and Talented!!! thank you!!

[@QuocDatPhung]

Thank you so much! I'm really happy my explanations are helpful! Please find all of my Calculus videos attached in this playlist: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@user-yr8kc8xd3i]

Thank you for taking the time to create this video.

[@QuocDatPhung]

It's my pleasure! Please kindly subscribe and share with your classmates! Here's the rest of my Calculus videos in a playlist: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@notavailable773]

This is so well explanation. Thanks 😊

[@QuocDatPhung]

Thank you NotAvailable :)!! I'm really glad you enjoyed my video! I would really appreciate if you could share with your classmates or kindly subscribe ~ you can find all of my Calculus II videos in this link: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@amalas1212]

😊😍Thank you and keep going ❤❤❤. I follow you from Jordan

[@QuocDatPhung]

Thanks so much Amal! Please don't forget to subscribe and share with your classmates :) I want these videos to help others too! As well, you can find the rest of my Calculus videos in this playlist: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@SN-ow1bp]

amazing video, do you have any videos covering the latter topics of calc 2 such as series and partial derivatives?

[@QuocDatPhung]

I'm working on those! For the moment I have more than 30 videos in my Calculus 2 playlist: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@na.1221]

Thanks teacher

[@QuocDatPhung]

Thank you Nardos! Your comments mean a lot to me :;))))

[@na.1221]

​@@QuocDatPhung oh! but please don't forget your promise in English grammar because I will be expect any time!

[@QuocDatPhung]

@@na.1221 In two weeks, I will start to make some English videos! Coincidentally, my friend is an English teacher and she's also asking me to make some English videos too! I will start with the basics: alphabets, learn about days of the weeks, days of the months, different names for colors, etc. Please let me know if you have specific topics in mind.

[@na.1221]

@@QuocDatPhung Those are very very simple. can you will be work it like conditional sentence, relative pronoun, diphthongs, articles, preposition, adverb, demonstrative pronoun, conjunction, tenses, auxiliaries, reported speech, passive and active voice, punctuation and so on.

[@QuocDatPhung]

@@na.1221 Thanks for your input. I will try my best.

[@nic4090]

Dumb question, but how come we don't subtract here? 33:07 because don't we subtract the missing middle space?

[@QuocDatPhung]

Hi Nic, what missing space are you referring to?

[@nic4090]

Sorry, my fault. I just realized we're applying the Disk Method, not the Washer Method. For some reason, I thought they were the same thing.

[@QuocDatPhung]

@@nic4090 I believe they are the same thing. I have a video on the trick when to use dish washer method v.s cylindrical shell. It's the first video in the link, I hope this would help: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@Abid-qp2jm]

tankoo tankoo

[@QuocDatPhung]

I'm glad it helped! Don't forget to subscribe and share with classmates!