Shell Method - Volume of Revolution

This calculus video tutorial focuses on volumes of revolution. It explains how to calculate the volume of a solid generated by rotating a region around the x axis, y axis, or non axis such as another line parallel to the x or y axis using the shell method or simply cylindrical shells. This video shows you how to write the radius and height function in terms of x and y by the use of a rectangle or shell. This tutorial contains plenty of examples and practice problems including those with two functions.

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[phantomwarden]

I am a chemistry major and have been watching your videos for 2 years. You’ve helped me so much that I believe I have spent more time watching you than in the classroom lol. Thank you for this

[easonxiao]

Somehow this guy knew my Calc final was coming up

[godfraydionzon]

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[lyndseystrait]

2:21 Shell method formula for when y-axis is axis of rotation (1st part when only 1 line vs 2nd part when 2 lines) and 4:26 Shell method formula for when x-axis is axis of rotation (1st part when only 1 line vs 2nd part when 2 lines). Fantastic examples and video!

[epictrooper]

Wow this was uploaded right when I started volume revolution perfect timing.

[kaushikkalesh]

Fun Fact - His most popular (most-viewed) video is not even about organic chemistry, it's about math lol

[bananapudding]

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[kara]

Calc Class: ok we are on the topic of the shell method
The Organic Chemistry Tutor: makes this video
The stars: have aligned

[georgesadler]

Professor Organic Chemistry Tutor, thank you for an awesome video/ lecture on the Shell Method in Calculus Two. The Shell Method is fairly simple to follow and understand from start to finish. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

[TheJollyRhino]

Thank you Thank you Thank you. I kept boggling my head trying to understand why my rotations weren't coming out right. No one ever said discretely that rotations about y HAVE to be in terms of x, and vice versa for rotations about x. So so helpful

[utilizator]

I have never been wondering how to find the volume when rotating around y axis. I am happy that I have learned a method to do this.

[rulinsky]

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[aragornxyz]

it is sad to see cut version here and now the original full upload being patreon exclusive video. (not only this video, many others) :c 10 dollar is bit too much for me (local economy). But still i am pretty much thankful for the videos, for your big effort to teach us, even if they are "necessary" part only :D

[abrahamortiz]

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[aardvarkansas]

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[maryangier]

at 4:25, shouldn't the bottom problem have f(y) and g(y) as the two functions rather than f(x) and g(x)? Were using the shell method and revolving around the x-axis- therefore, we need to integrate with respect to y... right?

[bread]

This dude has been saving my grades for 3 years