Shell Method - Volume of Revolution
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- Опубліковано 4 січ 2021
- 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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Full 54 Minute Video on UA-cam:
• Shell Method - Volume ...
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Direct Link to The Full Video: bit.ly/3zqHsOZ
The link on patron doesn't work, I have a subscription.
Fun Fact - His most popular (most-viewed) video is not even about organic chemistry, it's about math lol
Fun fact - no one asked
@@isaacsilva4301your fact kinda sucks tho
So true😂😂
@@isaacsilva4301🤣
You get everything you want even Chemistry, learn to appreciate him for doing this for us all who need help.
Somehow this guy knew my Calc final was coming up
Your finals are in the beginning of the semester?
@@micahgodsey455 My school had the finals after winter break so yeah
@@easonxiao6169 That sounds horrible
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
How do you enjoy chemistry? I am currently a space science major and considering either a double major for mathematics, chemistry, or biology.
I love math but I am also interested in other physical sciences.
@@codymorgan8812 Im double majoring in pure mathematics and physics. Regarding mathematics, you can choose between applied math and pure math. Pure math is a bit more different than applied math, but it is really awesome (at least for me). I encourage you to take an advanced class of whatever major you're interested in (if you can), in order to see which area you enjoy most. Also seeing the roadmaps for each major is helpful
The stuff he covers only cover the really basics of chemistry though
of all the sciences chemistry was my least favorite, and because of that it was one of the hardest. one thing that really helped me to enjoy chemistry over time was applying it to anatomy, and how different medicines and treatments and chemicals set off chain reactions in the human body. just helped me to appreciate chemistry a bit more@@codymorgan8812
Sir I'm really thankful to you. I have been struggling lately on these application of integral but ur videos really do help. My teacher is great but sometimes I can't just understand what she's trying to explain that's why I always run to your channel. Thank you Sir, I appreciate what u're doing.
Calc Class: ok we are on the topic of the shell method
The Organic Chemistry Tutor: makes this video
The stars: have aligned
Literally same wtf
Calc 2 is usually taught this time of year. He is simply making the video in a time where it will get the most views and bring in the move $$$.
You: are cute
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!
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 UA-cam TV with the Organic Chemistry Tutor.
Wow this was uploaded right when I started volume revolution perfect timing.
I began this week.
Niggas bro
@@Sant270 began on monday lmaooo.
Organic chem gets bitches bro
I'm going to buy your mug just to support you, you are literally my math savior, how are you so good at explaining things. It's like magic.
Not really, you should go to eddie woo’s channel for real magic
@@marq6325 subjective!
this guy is literally carrying me through my engineering degree
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.
I love your videos!! I’m a Mathematics teacher in Spanish, but now thanks to you, I know how to teach Math in English. Thanks 🎊🎉🎵❤️
My man just helped me pass university
you give me hope to keep going... much love, thank you!
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
first 2 minutes in and you already took my professors job.
whenever i have trouble, you always seem to know how to explain it well. thank you organic chem tutor
When I pass Calc 2 it'll be because of you!
Thanks!
i really appreciate your videos. Keep it up!
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
You're a lifesaver, thank you for all these amazing videos!!!
If i could give you a million dollars I would, you are honestly the best at explaining such complicated topics.
i wouldnt
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@@beachwave5705 fr lmao
@@jawadzahid24 why tf would i give someone 1,000,000 fucking dollars
Your videos are the best things ever I swear!!!!!
Thank you, this really helped me.
cant believe it was this easy. absolutely aced a quiz right after watching this thank you man
You explained it very well!
This dude has been saving my grades for 3 years
Love your videos, thank you!!
Awsm explanation .. I have a problem in solving height in two figures. But now it's clear❤️❤️❤️
Thank you, this saved my life
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?
thank you for the great video and effort ❤
Thank you so much for this. I really needed this today.
Helped me a lot, ty
This guys upload quota is insane
okay these are great example for entry level of the topics can you find example using a different axis of rotation
This guy singlehandedly gets me through college
This man is going to get me through college
at 3:40 radius and height should be in terms of x you say but it's R(y)*h(y)dy
This guy is better at explaining Calculus than some of my university professors, absolute goat
Very helpful !!
Thanks it helped me a lot
Thank you so much.
Thank you so much, you have saved me from the wrath of my Calculus II class!
I hope college board blesses up with a question about this, that would be pretty epic
You are the great man in the world
so good !!!
Thanks for everything
thanks, post also videos involving rotation about lines not parallel to x or y axis
yeah i like how all the nessesary complicated stuff is behind a paywall
Nice teaching
UR BACK I LOVE U THANK U PLS DO MORE SAT PREP THANKS HAVE A GOOD DAY
how is he back wtf
@@meffed he was on a break for months
can u do a live stream and live doughts let that new voting thing on youtube decide what topic? (no pressure)like for a live stream
There is a flaw at the 2:59 mark when rotating around the x-axis. While the radius is described by y and the thickness of the shell is described by dy, the height of the rectangle cannot be measured with this orientation. The method of cylindrical shells does not work here. The method of disks and washers is more versatile, and I also find it easier.
you make it look very easy compared to my prof, goat!
thank you so much
Keep it up👍
Thank you Sir
Thank you.
14:00 you always come when I need you the most
Hi! What if the Semicircle is from x=-2 to x=2? can we still use the cylindrical shell method?
could you explain why the r=x, instead of r=4-x in the first problem?
Thank you
Yo idk if u read my comment about uploading more calculus 2 in the last video, but if you did thank you.
I thank you so much for breaking this down this one made me want to bash my head in
I would marry this man- the way he’s saved my life so many times 😭😭😭
3:06 if I'm tryna find the volume of a cup which do I use rotation on the x axis or the y axis
i wish there was more practice but i think i get it enough
how do you solve when you rotate the region bounded about some value of y or x axis .....eg ,and rotated about the line x=4, then how do you find the radius ?
Are we just gonna ignore the fact that this guy almost knows how to solve all of the problems in math-
Every math teacher know all though lol
God bless you bro
Where do people like you even come from? Excellent video.
Good afternoon,sir I ask a question
* Write the limitations of disk method, cylindrical shell method and washing method to find a volume*
wouldn't x*x^3 be concave up on 0
Is the radius for these problems always x
Thank u
where does one find you to thank you in person?
ty
I never understood this section during my calc 2 class last semester, thank god most of it wasn't on my final. Btw, will you be uploading calc 3 content?
It would be an interesting topic to cover, especially on Laplace transform and Z transform.
I think he's uploaded some Calc 3 content in the past.
@@Cipher6i8 Thanks for letting me know! I'll try to find some as a review before the semester starts.
Explain to me why we have used 2pi and not just pi like in disk method
Bro, what happened to the old videos the ones that were 45 min and 2 hours long? Every time I wanted to make sure I was on point I used to look at them, stop the video, set up the integral (look at yours) and then go on to the next. Please bring them back.
He still makes those but they're now on Patreon. I wish I could get the full video but I can't really afford Patreon.
Legend
wait im confused are we finding the area of the rectangle or the region without the rectangle???
4:00 I do not think f(x) and g(x) can be functions of x. It seems to me that they both fail the vertical line test.
where does the 2pi come from here?
Hey! It's 2pi because it's a cylinder. Shell method is for cylinders.
A little late but exactly as laila said, the 2π is basically derived from the formula of a hollow cylinder which is 2πrh
If you use disk method will it give the same answer
watching this the night before the calc bc exam am i cooked?
I got my Daily Quiz right this time. Less fucking goo!!! Lifesafer for real!!
very helpful! How do you know where the axis of rotation is?
The problem should tell you! Something like rotate the curves about the x axis
Sir can I Recommend a Topic it's about Axiomatic System
So the radius is always=x ?
the way the college book explained it was so hard. x being the average radius makes no sense
nevermind i got it
How do i know whether to use shell method or disk washer 😢😢
At 4:26, why didnt you write h(y)= f(y) -- g(y) ??
this is part is really tough tbh
nice
Does the shell method always have 2pi before the integral, compared to the disk/washer's method of only being 1pi before the integral
yes
At 4:25, it should say h(y) = f(y)- g(y), not f(x) - g(x)
Technically when talking about rotating around the x, the f(x) and g(x) you drew aren’t functions even though you called them function.