Volume of Solid of Revolution Shell Method Calculus 1 AB 3 Examples
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- čas přidán 5. 08. 2024
- If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage / profrobbob I introduce finding the volume of revolutions using the Shell Method and through 3 examples compared it to the Disk and Washer Method. NOTE: There is a copy error at minute 24:00, 192/5 pi is not equal to 4632.47!!!
EXAMPLES at 10:36 15:17 20:12 24:20 28:30 Find free review test, useful notes and more at www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage / profrobbob
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I've watched many of your calculus videos without commenting. That being said, I have to thank you for your incredible explanations and in-depth lessons. I've never had any trouble with a math class prior to calculus 2, but your videos help me to master the methods that we are learning quickly. As a student of astrophysics, I know the road will only get tougher from here, and I thank you, Mr. Tarrou, for the help you have provided a great number of individuals through your youtube lectures. You deserve so many more subscribers than you have.
Micah Goulart
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I'm happy to hear that my videos have helped you so much even though it sounds like we have almost completed our journey together after you finish Calc2 :(
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+hingo that just means there must be too much time between videos...lol
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This. Is. So. Simple.
Sometimes I feel like our calculus teacher could make addition seem confusing. This is so simple, our teacher made it sound impossibly confusing.
Thank you for the help.
You're welcome ThePieMan305 glad you found it helpful and less confusing:)
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You are hands down the best math teacher on youtube. Your passion for mathematics really shows and it makes the difference between a boring lesson and an interesting lesson for me.
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thanks for your videos, im from chile(south america) im studding civil engineering and let me tell you that your method of teach is really clear and friendly with the listener, thanks again and please never stop doing this :D
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This content is proof that calculus and calligraphy can mix (beautifully)!
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This review was amazing, thank you for explaining the math so clearly without dumbing it down too much or being incredibly dry like so many math teachers on CZcams. This helped me so much and I’ll definitely be coming back for help with other topics in the future :)
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25:56 Natural mishap. but still hilarious!!! lol "I want the dix" Studying calculus and I needed a little comic relief... and some dix
These videos are very well put together, and very informative. good job
+Roalled gold THANKS!
Great drawing + great teaching = wonderful video! Glad that I found this video, it really helped me cleared my doubts on determining the radius, height, inner radii, and outer radii! :)
I love your math problem Cinnara !
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Absolutely great explanation of this volume business. Thanks for the video.
Thank you for watching and your kind feedback.
Thank you for making this video! it really helped.
You're welcome and thanks for studying and subbing too!
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Professor RobBob , I understand the Shell Method much better than the Disk and Washer Method in Calculus Two. The best way to learn this method is to practice and recognize a pattern for these volume problems. Drawing a picture of the problem also helps with finding solutions.
Thanks a lot ProfRob
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your videos always help, I've been following you from precalc moving up to calc2 and now I wonder if you have like study guides that stick with your videos with more supporting examples so I wouldn't need to go back to my instructor as she's making my life harder. Thank you again and I'm kind of jealous how your brain can store all of this math... you're my pacemaker!!!!
+Isaac Sallam thanks for all you past support!
Sorry to say, I do not have any study guides available...it's all I can do to keep new videos coming during the school year:(
Great video
thanks a lot. you're better than my lecturer at teaching! (+ drawing and lettering...).
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thank you for this!! i learned a lot😊
you're welcome...thanks for learning!
great video helped tremendously
+craig lastly thanks for liking, studying and subbing too:)
New Closed Captioned #math Volume of Solid of Revolution Shell Method
Thank you Sir.
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Love ur videos
:)
Thank you! Your awesome!
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very nice!!!
thanks for watching!
Sir, mind if I ask how old you are? You don't seem to have lost any energy at all compared to your videos from 2+ years ago! I thank you for all of the hard work you put into your videos, you've helped me tremendously over the last year!!
42 and proud of every gray hair! Thanks for being such a loyal subscriber Neoraider0786 and that's great to hear because I actually feel even more passionate about growing this channel and adding to my playlist with every video I make! Teaching on CZcams and helping students all over the world is more than I ever dreamed possible 2+ years ago and now my wife and I have made it our goal to someday see a "M" next to our subscriber count...always dream BIG!
thanks for that video. 😇
:)
The shell's height is equal to the area between two curves which is f(x) minus g(x) or top function minus bottom function
In terms of y ....the shell's height is equal to the right function minus left function
How do you determine if you should do the problem with respect to y or x? In your last example you took it with respect to y instead of x even though the plane region was being rotated about the x-axis. Was this because you were implementing the shell method?
I'm having trouble understanding why p(x) commonly is just x, or the "upper bound - x"
Since the radius (distance along x-axis) appears to a constant, why do we call it x?
i dont get how the radius is 6-x at 26.5 minutes exemple. Isn't there a hole from x=4 to x=6, so shouldn't it be 4-x?
thats really good drawing,, like i mean look at all the detail. wow....
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Well, I stop at the very beginning of the video coz his drawing is too good and I had figured everything out by the picture
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Wait, at around 8:00 you were talking about how the formula is similar to the formula fro surface area. But isnt the integral of x just x^2/2? So when you say 2*pi*integral(radius) * height, this is just 2*pi*radius^2/2*height, or pi*radius^2*height. Is there a mistake in my reasoning?
So the cylinder shell method is basically adding together a bunch of straws with an infinitely small width? But isn't the width of the straw, or cylinder shell, effectively equal to the radius?
Hello, I am just wondering in the first shell method example. How did you manage to figure out that y=1/3(x^2)+1 height of the region to be 4? Also how did you find out where they intersect? Did you just interpret from the graph?
+Jahmere11 He got 4 because his upper limit is 4. on the y-axis. You can get the intersection points algebraically by using substitution or elimination techniques (Algebra) using the given system of equations. Hope this helps!
Quite helpful! Thank you sir. I seem to get confused with when determining respect to y or x! Annoying.
THANK YOU Jeton Koka for watching and being the first to comment on this video...glad you found it helpful!
what does k stand for?
nyc one
Thank you so much :)
+Lindsay Lumbera :)
Oh my goodness! #fangirling right nowwwwwwwwwwwww!
+Lindsay Lumbera
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Thank you for answering my question. My professor for calc 2 merely puts long extended proofs on the board in class and we have time for only ONE example no questions. Basically, I'm teaching myself with your wonderful videos and Paul's Online Notes. :D
It sounds like you will be at the end of my videos soon if not already:( Have you tried the intergralCalc channel for more examples? I have a link to her channel on my channel's homepage. I had college professors like your's as well. With your determination I am sure you are going to do awesome:D Thank you for watching and all your support! Please return the favor and spread the word to all your friends.
I just went to Paul's Online Notes. What a great resource:0 Thanks for sharing.
Oh yes I've already told my peers who are in the same situation I'm in. I'll try that channel as well. I have most of my notes based on your channel I'll check her's as well. I'll be using both as my major resources this semester i have to get an A.
You're welcome. Hope it helps others as well.
Is it possible to compute the volume of the irregular shape of an object? for example; how can I get the volume of the tree?
+Jhon Marc Mamuyac No pro here, but someone in my class someone asked our teacher the same thing he said it's possible if you fixed an equation to mimic the shape (in the case the tree) that you wanted and went from there. He said that for most irregular shapes that since making the equation fit is pretty difficult that other methods are better, for example putting the shape in water and measuring the physical change in volume :D
+Jhon Marc Mamuyac No pro here, but someone in my class someone asked our teacher the same thing he said it's possible if you fixed an equation to mimic the shape (in the case the tree) that you wanted and went from there. He said that for most irregular shapes that since making the equation fit is pretty difficult that other methods are better, for example putting the shape in water and measuring the physical change in volume :D
+Jhon Marc Mamuyac
Like someone else said, you absolutely could find the the volume of any object as long as you know the functions that cause their irregularities. The simplest method would just be the displacement method however.
I'm confusing the shell method and the washer method. Wouldn't any hole in a disk be a cylinder or a washer in some way? This is giving me trouble.... I don't know which one to use when there a whole in the middle...
use shell method when your rectangle is parallel to the axis of rotation, and use the washer method when the rectangle is perpendicular to the axis of rotation
Dylan Greer Thank you for the help!!!
Prof, Kind of off-topic but google does not yield a discernible easy to understand answer. Are summations and integration's essentially the same thing? Integrals work like logic loops, to my understanding just like summations?
Well, I know nothing about logic loops. Estimating area with Riemman Sums is estimating area with some rectangles. Then we let the number of those rectangles reach infinity and then definite integrals.
+Kevin Anthony In the most summarized sense, a limit of a summation is an integral.
Does it matter whether you choose the shell or disc method?
+Elphaba Crux Often one method will be easier than the other for a particular problem, so choose the most efficient method.
THANK YOU!!!!
+Elphaba Crux :)
Do you say heidth? for height?
I did mean HEIGHT and apologize if that is not how it sounds:(
Hey mr tarrou. You always say you want a big 'M' next to your youtube name but what does it mean?
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how can I donate 50 dollars to thank you for all the videos
There is a "TIP THE TEACHER" button at the top right hand corner of the banner on my home page if you are still feeling generous:) We do appreciate donations from our viewers and put the money back into improvements to our channel as we can.
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Where did 4 come from?
???
During what time reference in the video?
when i calculate i get 27/4 not 27/2
(-1/12)*3^4 + (3/2)*3^2 = 27/4
You forgot to multiply at the end by 2pi which reduces to 27pi/2.
Can your students write and draw like you do (I assume they can because they see you everyday).
Please teach us how to write and draw like you do -- most importantly how to write.
I never assume Eggs Benedict :(
Some of them do I'm sure, but you never really know how much impact you are making.
Please check out my website that includes my cursive videos and a practice sheet at www.profrobbob.com and the only drawing I've learned is from 19 years go teaching:)
this mans looks like mr. bean
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As with most videos in the topic, in my opinion, you are failing to address maybe the most important point, which is when one has no choice but to use the shells method in order to find the volume.
32:03 his hostages attempt to escape
That was our 5lb attack dog:)
kazam!!
+Perdi Manal or BAM!!!
25:53 ;)
I don't think 192/5 Pi is equal to 4632.47, no matter how many ways I try it.
TraleeFair I caught that copy error in my other lesson, but missed here. Thank you very much!!!
Einsteins grandson
+Amirhosseine Dokhanchi LOL!!! ...still laughing!
I haven't heard that one yet...but it was a good one!!
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nice haircut
bbbbammm!