Shell Method - Volume of Revolution

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  • Опубликовано: 26 авг 2024
  • 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:
    / mathsciencetutor
    Direct Link to The Full Video:
    bit.ly/3zqHsOZ
    ____________________________________
    Full 54 Minute Video on RUclips:
    • Shell Method - Volume ...
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    bit.ly/46xaQTR

Комментарии • 209

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  2 года назад +32

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

  • @easonxiao6169
    @easonxiao6169 3 года назад +362

    Somehow this guy knew my Calc final was coming up

    • @micahgodsey455
      @micahgodsey455 3 года назад +4

      Your finals are in the beginning of the semester?

    • @easonxiao6169
      @easonxiao6169 3 года назад +10

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

    • @zzzluvsk
      @zzzluvsk 3 месяца назад

      @@easonxiao6169 That sounds horrible

    • @LeagueJeffreyG
      @LeagueJeffreyG 28 дней назад

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

  • @kaushikkalesh1678
    @kaushikkalesh1678 3 года назад +494

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

    • @isaacsilva4301
      @isaacsilva4301 11 месяцев назад +25

      Fun fact - no one asked

    • @NotSoStNick
      @NotSoStNick 11 месяцев назад +1

      @@isaacsilva4301your fact kinda sucks tho

    • @user-nk1hm3jl5g
      @user-nk1hm3jl5g 11 месяцев назад +3

      So true😂😂

    • @RCKola281
      @RCKola281 11 месяцев назад +5

      @@isaacsilva4301🤣

    • @entertainmentalloverthewor565
      @entertainmentalloverthewor565 11 месяцев назад +9

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

  • @phantomwarden8145
    @phantomwarden8145 Год назад +147

    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
      @codymorgan8812 Год назад +2

      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
      @mapi100 Год назад +3

      @@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
      @peelysl 11 месяцев назад

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

    • @forthehomies7043
      @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
    @godfraydionzon9539 3 года назад +167

    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.

  • @kara4773
    @kara4773 3 года назад +298

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

    • @corbynkutak2898
      @corbynkutak2898 3 года назад +1

      Literally same wtf

    • @epod3422
      @epod3422 3 года назад +3

      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
      @DennisBolanos 3 года назад +2

      You: are cute

  • @lyndseystrait1513
    @lyndseystrait1513 6 месяцев назад +9

    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!

  • @epictrooper2568
    @epictrooper2568 3 года назад +108

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

  • @bananapudding4854
    @bananapudding4854 3 года назад +83

    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
      @marq6325 3 года назад

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

    • @yugadeepk5297
      @yugadeepk5297 2 года назад +17

      @@marq6325 subjective!

  • @georgesadler7830
    @georgesadler7830 2 года назад +40

    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 RUclips TV with the Organic Chemistry Tutor.

  • @victorfernandez4082
    @victorfernandez4082 Год назад +11

    this guy is literally carrying me through my engineering degree

  • @utilizator1701
    @utilizator1701 3 года назад +24

    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.

  • @TheJollyRhino
    @TheJollyRhino 6 месяцев назад +1

    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

  • @rulinsky
    @rulinsky 3 года назад +8

    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 🎊🎉🎵❤️

  • @user-hdhdhhdhdhsnjdjdjdioowj
    @user-hdhdhhdhdhsnjdjdjdioowj 2 года назад +14

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

  • @aragornxyz8004
    @aragornxyz8004 3 года назад +64

    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

  • @bigt9203
    @bigt9203 Год назад +4

    My man just helped me pass university

  • @maryangier2773
    @maryangier2773 Год назад +6

    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?

  • @AnthonySalierno
    @AnthonySalierno Год назад +17

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

  • @celineguler
    @celineguler Год назад +3

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

  • @abrahamortiz2074
    @abrahamortiz2074 4 месяца назад

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

  • @bread1542
    @bread1542 2 года назад +2

    This dude has been saving my grades for 3 years

  • @user-jj3mj2qc4c
    @user-jj3mj2qc4c 3 месяца назад +1

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

  • @isoid
    @isoid 3 года назад +8

    This guys upload quota is insane

  • @SokumenTop
    @SokumenTop 3 года назад +5

    This guy singlehandedly gets me through college

  • @mel-if4fv
    @mel-if4fv 11 месяцев назад +3

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

  • @johnsymeonidis1313
    @johnsymeonidis1313 8 месяцев назад

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

  • @Clemfandang0
    @Clemfandang0 2 месяца назад

    Thank you, this really helped me.

  • @francisg.3797
    @francisg.3797 11 месяцев назад +1

    This man is going to get me through college

  • @aardvarkansas7500
    @aardvarkansas7500 3 месяца назад

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

  • @michaelli6934
    @michaelli6934 3 года назад +3

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

  • @plasma8321
    @plasma8321 3 года назад +5

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

  • @theyammi437
    @theyammi437 3 года назад +3

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

  • @realrishiiscoolgaming9548
    @realrishiiscoolgaming9548 3 года назад +8

    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

  • @tejansallu2287
    @tejansallu2287 3 года назад +3

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

  • @ineedasubmissiveboyfriend9236
    @ineedasubmissiveboyfriend9236 3 года назад +5

    Are we just gonna ignore the fact that this guy almost knows how to solve all of the problems in math-

    • @bonk2987
      @bonk2987 3 года назад +1

      Every math teacher know all though lol

  • @cruzsanchez5942
    @cruzsanchez5942 6 месяцев назад

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

  • @hmedina79
    @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.

  • @user-hv6ef9ie1g
    @user-hv6ef9ie1g 3 месяца назад

    You explained it very well!

  • @user-rz9gn9ce3m
    @user-rz9gn9ce3m 8 месяцев назад +2

    where does the 2pi come from here?

    • @lailaplaysdbd4004
      @lailaplaysdbd4004 8 месяцев назад

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

    • @bazellezb5559
      @bazellezb5559 3 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

  • @djcantskate3883
    @djcantskate3883 2 года назад +2

    Is the radius for these problems always x

  • @hassanfarraj6
    @hassanfarraj6 10 месяцев назад +1

    So the radius is always=x ?

  • @seer873
    @seer873 Год назад

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

  • @nadineelzeidy9242
    @nadineelzeidy9242 3 года назад +2

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

    • @meffed
      @meffed 3 года назад

      how is he back wtf

    • @nadineelzeidy9242
      @nadineelzeidy9242 3 года назад

      @@meffed he was on a break for months

  • @GooseCrack
    @GooseCrack 2 года назад

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

  • @masonp5
    @masonp5 3 года назад +1

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

  • @Josue-Arreaga
    @Josue-Arreaga 3 года назад +3

    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
      @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.

  • @pranjalchand6792
    @pranjalchand6792 4 месяца назад

    Thanks it helped me a lot

  • @titicaca315
    @titicaca315 Год назад

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

  • @mondainist
    @mondainist 3 года назад +4

    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
      @utilizator1701 3 года назад

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

    • @Cipher6i8
      @Cipher6i8 3 года назад +2

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

    • @mondainist
      @mondainist 3 года назад

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

  • @khalidalq3334
    @khalidalq3334 2 года назад

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

  • @pentagonperry
    @pentagonperry 3 года назад +1

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

  • @brandonhung9990
    @brandonhung9990 3 года назад +2

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

  • @minnil7927
    @minnil7927 Год назад +1

    Not clear on what R is and how to find it

  • @Duaaaa786
    @Duaaaa786 3 года назад +3

    i really appreciate your videos. Keep it up!

  • @TheLargestwinter3
    @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

  • @In_himystyle
    @In_himystyle 3 года назад

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

  • @somebodyoncetoldme8636
    @somebodyoncetoldme8636 11 месяцев назад

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

  • @Life-zm6iz
    @Life-zm6iz 2 года назад +1

    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.

  • @noone-xs8om
    @noone-xs8om 2 года назад

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

  • @Ballman100
    @Ballman100 3 месяца назад +2

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

  • @yohannamachado8505
    @yohannamachado8505 5 месяцев назад

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

  • @tumelomokgojane5648
    @tumelomokgojane5648 11 месяцев назад +1

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

  • @andrews5831
    @andrews5831 3 года назад +3

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

  • @3lackman761
    @3lackman761 Месяц назад

    If you use disk method will it give the same answer

  • @ididmuhammed4086
    @ididmuhammed4086 2 года назад

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

  • @embin_2129
    @embin_2129 9 месяцев назад

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

  • @ahn4951
    @ahn4951 4 месяца назад

    so good !!!

  • @jdums8534
    @jdums8534 3 месяца назад +1

    this is part is really tough tbh

  • @554poonam7
    @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*

  • @bieelzzin
    @bieelzzin 2 года назад

    Helped me a lot, ty

  • @MoguMogu818
    @MoguMogu818 Год назад

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

  • @noornayel3394
    @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

  • @ziaudzoheb1860
    @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 ?

  • @jeremie2599
    @jeremie2599 3 года назад

    You are the great man in the world

  • @plopperspal8494
    @plopperspal8494 8 месяцев назад

    Thank you.

  • @lemmepaturhead8651
    @lemmepaturhead8651 9 месяцев назад

    Thank you

  • @matthewlee3520
    @matthewlee3520 3 года назад +1

    Thank you so much for this. I really needed this today.

  • @philomatta2620
    @philomatta2620 2 года назад

    thank you for the great video and effort ❤

  • @logical1037
    @logical1037 2 года назад

    Thanks for everything

  • @hystericalnigga12345
    @hystericalnigga12345 7 месяцев назад

    God bless you bro

  • @StudybyYourselfPLUS
    @StudybyYourselfPLUS 3 года назад

    Thank you so much.

  • @meeee3838
    @meeee3838 2 года назад

    At 4:26, why didnt you write h(y)= f(y) -- g(y) ??

  • @mrmansir3734
    @mrmansir3734 Год назад +1

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

  • @gamesnaturesite5901
    @gamesnaturesite5901 3 года назад

    Nice teaching

  • @nqubekogcwensa2840
    @nqubekogcwensa2840 2 года назад

    where does one find you to thank you in person?

  • @jileelab5696
    @jileelab5696 2 года назад

    Hi! What if the Semicircle is from x=-2 to x=2? can we still use the cylindrical shell method?

  • @shatararuiz2653
    @shatararuiz2653 3 месяца назад

    is r always equal to x?

  • @OlegAltukhov
    @OlegAltukhov 2 года назад

    Love your videos, thank you!!

  • @mrmansir3734
    @mrmansir3734 Год назад +3

    at 2:28 it was mentioned a and b are representing x values, but at 6:21, the bounds are labelled as a and b, but the bounds include 1 y value, and 1 x value, so shouldn't the bounds be d and c for the example at 6:21?

  • @jicheolha7313
    @jicheolha7313 2 года назад

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

  • @MazdaFantasma
    @MazdaFantasma 2 месяца назад +1

    guys we are getting something from here it not fair not to like this

  • @voltysaysno5355
    @voltysaysno5355 Год назад

    Is the radius always going to be x/y?

  • @jaewanjang4469
    @jaewanjang4469 3 года назад

    Very helpful !!

  • @Emily-yq4bl
    @Emily-yq4bl 3 года назад

    thank you so much

  • @RunedGolem1
    @RunedGolem1 2 года назад +1

    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.

  • @gur0004
    @gur0004 3 года назад +1

    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.

    • @suhailraja7797
      @suhailraja7797 Год назад

      I know you're probably done with this class 😂 but he said if it's the x axis it must be in terms of y you just misheard him

  • @tonjohn_
    @tonjohn_ 3 года назад +2

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

  • @KhanKhan-ux2ss
    @KhanKhan-ux2ss 2 года назад

    Thank you Sir

  • @hextech1172
    @hextech1172 3 года назад

    Sir can I Recommend a Topic it's about Axiomatic System