Shell Method - Volume of Revolution

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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.
Full 54 Minute Video on Patreon:
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Direct Link to The Full Video:
bit.ly/3zqHsOZ
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Full 54 Minute Video on RU-vid:
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17 сен 2024

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Комментарии : 212

@TheOrganicChemistryTutor 2 года назад

Full 54 Minute Video on Patreon: www.patreon.com/MathScienceTutor Direct Link to The Full Video: bit.ly/3zqHsOZ

@abulkhaiyrtalapov3038 Год назад

The link on patron doesn't work, I have a subscription.

@easonxiao6169 3 года назад

Somehow this guy knew my Calc final was coming up

@micahgodsey455 3 года назад

Your finals are in the beginning of the semester?

@easonxiao6169 3 года назад

@@micahgodsey455 My school had the finals after winter break so yeah

@zzzluvsk 4 месяца назад

@@easonxiao6169 That sounds horrible

@LeagueJeffreyG Месяц назад

@@micahgodsey455 these things are learned in different intervals, the volume of Revolution is normally chapter 6 but is sometimes introduced sooner

@phantomwarden8145 Год назад

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

@codymorgan8812 Год назад

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.

@mapi100 Год назад

@@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

@peelysl Год назад

The stuff he covers only cover the really basics of chemistry though

@forthehomies7043 6 месяцев назад

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

@godfraydionzon9539 3 года назад

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.

@kaushikkalesh1678 3 года назад

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

@isaacsilva4301 Год назад

Fun fact - no one asked

@NotSoStNick Год назад

@@isaacsilva4301your fact kinda sucks tho

@AmazingDerick 11 месяцев назад

So true😂😂

@RCKola281 11 месяцев назад

@@isaacsilva4301🤣

@entertainmentalloverthewor565 11 месяцев назад

You get everything you want even Chemistry, learn to appreciate him for doing this for us all who need help.

@lyndseystrait1513 7 месяцев назад

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!

@kara4773 3 года назад

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

@corbynkutak2898 3 года назад

Literally same wtf

@epod3422 3 года назад

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 $$$.

@DennisBolanos 3 года назад

You: are cute

@epictrooper2568 3 года назад

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

@Sant270 3 года назад

I began this week.

@CountChokcula 3 года назад

Niggas bro

@grandking8338 3 года назад

@@Sant270 began on monday lmaooo.

@antoinnelamah6949 3 года назад

Organic chem gets bitches bro

@georgesadler7830 3 года назад

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 RU-vid TV with the Organic Chemistry Tutor.

@bananapudding4854 3 года назад

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.

@marq6325 3 года назад

Not really, you should go to eddie woo’s channel for real magic

@yugadeepk5297 3 года назад

@@marq6325 subjective!

@user-hdhdhhdhdhsnjdjdjdioowj 2 года назад

If i could give you a million dollars I would, you are honestly the best at explaining such complicated topics.

@beachwave5705 2 года назад

i wouldnt

@AzureSwiper Год назад

@@beachwave5705 🤣

@jawadzahid24 Год назад

@@beachwave5705 fr lmao

@beachwave5705 Год назад

@@jawadzahid24 why tf would i give someone 1,000,000 fucking dollars

@utilizator1701 3 года назад

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 3 года назад

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 🎊🎉🎵❤️

@AnthonySalierno Год назад

When I pass Calc 2 it'll be because of you!

@TheOrganicChemistryTutor Год назад

Thanks!

@maryangier2773 Год назад

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?

@victorfernandez4082 Год назад

this guy is literally carrying me through my engineering degree

@bigt9203 Год назад

My man just helped me pass university

@TheJollyRhino 7 месяцев назад

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

@aragornxyz8004 3 года назад

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

@celineguler Год назад

at 3:40 radius and height should be in terms of x you say but it's R(y)*h(y)dy

@abrahamortiz2074 5 месяцев назад

whenever i have trouble, you always seem to know how to explain it well. thank you organic chem tutor

@michaelli6934 3 года назад

you give me hope to keep going... much love, thank you!

@aardvarkansas7500 4 месяца назад

You're a lifesaver, thank you for all these amazing videos!!!

@bread1542 2 года назад

This dude has been saving my grades for 3 years

@mel-if4fv Год назад

could you explain why the r=x, instead of r=4-x in the first problem?

@tejansallu2287 3 года назад

14:00 you always come when I need you the most

@carlosgarcia-q8l 4 месяца назад

first 2 minutes in and you already took my professors job.

@hmedina79 2 месяца назад

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.

@admmv3admmv3 9 месяцев назад

where does the 2pi come from here?

@lailaplaysdbd4004 9 месяцев назад

Hey! It's 2pi because it's a cylinder. Shell method is for cylinders.

@bazellezb5559 4 месяца назад

A little late but exactly as laila said, the 2π is basically derived from the formula of a hollow cylinder which is 2πrh

@Clemfandang0 2 месяца назад

Thank you, this really helped me.

@cruzsanchez5942 7 месяцев назад

Your videos are the best things ever I swear!!!!!

@realrishiiscoolgaming9548 3 года назад

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

@user-hv6ef9ie1g 4 месяца назад

You explained it very well!

@SokumenTop 3 года назад

This guy singlehandedly gets me through college

@isoid 3 года назад

This guys upload quota is insane

@francisg.3797 Год назад

This man is going to get me through college

@theyammi437 3 года назад

Thank you so much, you have saved me from the wrath of my Calculus II class!

@Josue-Arreaga 3 года назад

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.

@oluwaseyiikujuni9382 2 года назад

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.

@nadineelzeidy9242 3 года назад

UR BACK I LOVE U THANK U PLS DO MORE SAT PREP THANKS HAVE A GOOD DAY

@meffed 3 года назад

how is he back wtf

@nadineelzeidy9242 3 года назад

@@meffed he was on a break for months

@plasma8321 3 года назад

yeah i like how all the nessesary complicated stuff is behind a paywall

@johnsymeonidis1313 9 месяцев назад

This guy is better at explaining Calculus than some of my university professors, absolute goat

@seer873 Год назад

I would marry this man- the way he’s saved my life so many times 😭😭😭

@Duaaaa786 3 года назад

i really appreciate your videos. Keep it up!

@GooseCrack 2 года назад

cant believe it was this easy. absolutely aced a quiz right after watching this thank you man

@djcantskate3883 2 года назад

Is the radius for these problems always x

@pranjalchand6792 5 месяцев назад

Thanks it helped me a lot

@StudybyYourselfPLUS 3 года назад

Thank you so much.

@brandonhung9990 3 года назад

Yo idk if u read my comment about uploading more calculus 2 in the last video, but if you did thank you.

@mondainist 3 года назад

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?

@utilizator1701 3 года назад

It would be an interesting topic to cover, especially on Laplace transform and Z transform.

@Cipher6i8 3 года назад

I think he's uploaded some Calc 3 content in the past.

@mondainist 3 года назад

@@Cipher6i8 Thanks for letting me know! I'll try to find some as a review before the semester starts.

@hassanfarraj6 11 месяцев назад

So the radius is always=x ?

@TheLargestwinter3 2 года назад

okay these are great example for entry level of the topics can you find example using a different axis of rotation

@bieelzzin 2 года назад

Helped me a lot, ty

@khalidalq3334 2 года назад

you make it look very easy compared to my prof, goat!

@titicaca315 2 года назад

I thank you so much for breaking this down this one made me want to bash my head in

@MoguMogu818 Год назад

I got my Daily Quiz right this time. Less fucking goo!!! Lifesafer for real!!

@ididmuhammed4086 2 года назад

thanks, post also videos involving rotation about lines not parallel to x or y axis

@3lackman761 2 месяца назад

If you use disk method will it give the same answer

@In_himystyle 3 года назад

Awsm explanation .. I have a problem in solving height in two figures. But now it's clear❤️❤️❤️

@jeremie2599 3 года назад

You are the great man in the world

@embin_2129 9 месяцев назад

Explain to me why we have used 2pi and not just pi like in disk method

@pentagonperry 3 года назад

wouldn't x*x^3 be concave up on 0

@OlegAltukhov 2 года назад

Love your videos, thank you!!

@noone-xs8om 2 года назад

Where do people like you even come from? Excellent video.

@masonp5 3 года назад

I hope college board blesses up with a question about this, that would be pretty epic

@hystericalnigga12345 8 месяцев назад

God bless you bro

@logical1037 2 года назад

Thanks for everything

@Ballman100 4 месяца назад

watching this the night before the calc bc exam am i cooked?

@554poonam7 3 года назад

Good afternoon,sir I ask a question * Write the limitations of disk method, cylindrical shell method and washing method to find a volume*

@plopperspal8494 9 месяцев назад

Thank you.

@noornayel3394 Год назад

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

@ahn4951 5 месяцев назад

so good !!!

@lemmepaturhead8651 10 месяцев назад

Thank you

@philomatta2620 2 года назад

thank you for the great video and effort ❤

@yohannamachado8505 6 месяцев назад

wait im confused are we finding the area of the rectangle or the region without the rectangle???

@nqubekogcwensa2840 3 года назад

where does one find you to thank you in person?

@gamesnaturesite5901 3 года назад

Nice teaching

@somebodyoncetoldme8636 11 месяцев назад

i wish there was more practice but i think i get it enough

@tonjohn_ 3 года назад

Once I graduated, i'll donate alot of shit to this channel

@مانجاه 3 года назад

!RemindMe never

@locodannyboy 16 дней назад

appreciate it cuh

@andrews5831 3 года назад

the way the college book explained it was so hard. x being the average radius makes no sense

@andrews5831 3 года назад

nevermind i got it

@minnil7927 Год назад

Not clear on what R is and how to find it

@ziaudzoheb1860 Год назад

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 ?

@jaewanjang4469 3 года назад

Very helpful !!

@jicheolha7313 2 года назад

At 4:25, it should say h(y) = f(y)- g(y), not f(x) - g(x)

@Emily-yq4bl 3 года назад

thank you so much

@artforhaunting 3 года назад

very helpful! How do you know where the axis of rotation is?

@foxblaze11 3 года назад

The problem should tell you! Something like rotate the curves about the x axis

@tumelomokgojane5648 Год назад

How do i know whether to use shell method or disk washer 😢😢

@oooooo3820 2 года назад

You my good sir are my fucking hero!

@Life-zm6iz 2 года назад

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.

@obedpreveau9247 2 года назад

I call him the SAVIOR 😊😊😊😊

@nicolasbarker524 Год назад

Legend

@shatararuiz2653 4 месяца назад

is r always equal to x?

@jdums8534 4 месяца назад

this is part is really tough tbh

@KhanKhan-ux2ss 2 года назад

Thank you Sir

@mrmansir3734 Год назад

at 3:32, why are the bounds c to d instead of a to b?

@robincolpaert5047 Год назад

u can name them everything u want…

@gur0004 3 года назад

at 3:40 you said when rotating about the x-axis, the radius and height have to be in terms of x but then you expressed them in terms of Y! Confused asf.