Longer Version - Volumes using Cylindrical Shells

Поділитися
Вставка
  • Опубліковано 8 вер 2024
  • Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Problems with Detailed solutions made by me! :
    www.teacherspay...
    Longer Version - Volumes using Cylindrical Shells - In this video I do numerous examples of finding volumes using the shell method.
    For more free math videos, visit PatrickJMT.com

КОМЕНТАРІ • 425

  • @thomasm_complains
    @thomasm_complains 8 років тому +54

    Its sad that as university students paying thousands in tuition have professors that are so fundamentally bad we have to seek online teachers to help us. THANK GOD we have you patrick, without you i won't pass this calc2 class.

    • @Ji23da
      @Ji23da 7 років тому +8

      T Mccart imagine the hardship in the early 90's hahaaha where youtube is not that popular (or does not exist yet, not sure). They have to rely on their prof and book to pass this course.

    • @seankimbrough8489
      @seankimbrough8489 7 років тому

      didn't your father teach you how to read a textbook? teachers work better with the book

    • @ksale22
      @ksale22 7 років тому

      welp ya usually are just paying for the degree

  • @SpiritedBanana
    @SpiritedBanana 10 років тому +267

    I learned more in this 20 minute video than my 1 hr university lecture. Thanks Patrick!

  • @kenthumerickhouse9386
    @kenthumerickhouse9386 6 років тому +3

    Dropped that super casual bomb - "Always make your shell the parallel to your axis of rotation." That was amazing, and very helpful!

  • @beautypie23
    @beautypie23 8 років тому +20

    I've gotten two 100% scores in my Calc 2 class because of you. I always feel lost in lecture but you always make it so simple and easy to follow. I'm really thankful for your videos, you're awesome!

  • @makaires
    @makaires 10 років тому +26

    A friend of mine recommended your videos. I've been getting C's in calc lately, and for one who has never gotten below a B, I rather dislike that. Even 5 minutes in, it already makes more sense than when my calc teacher explains it. Thanks!

    • @patrickjmt
      @patrickjmt  10 років тому +17

      happy to help. i have tons of calc 2 and 3 stuff, so come back any time.

    • @pintoandre1807
      @pintoandre1807 7 років тому +3

      patrickJMT you are my senpai

  • @jow7775
    @jow7775 10 років тому +105

    You are such a better teacher than my Calculus teacher, thanks.

  • @Asadron
    @Asadron 9 років тому +50

    For anyone wondering, multiplying the 2pi in front comes from multiplying each shell cross section by the circumference of the shell (since circumference is 2pi*r, it just brings out the 2pi). That was something I didn't understand at first, so I thought I'd share it for anyone else who might be wondering :)

    • @XNagelX
      @XNagelX 9 років тому

      You mean circumference?

    • @Asadron
      @Asadron 9 років тому

      XNagelX Oops, circumference* Yes. Thanks for pointing that out!

    • @mubashirahmad6643
      @mubashirahmad6643 7 років тому

      XNagelX
      i dont under stand the concept of shell radius

    • @chadliampearcy
      @chadliampearcy 7 років тому

      I read your comment, didn't click, took a break, it clicked.

  • @happybuttonquail9603
    @happybuttonquail9603 8 років тому +11

    Thank you soooo much!!! If I pass my cal2 exam in 2 hours, it's all thank to you. Such simple concept, why cant teacher explain it simply like this.

  • @ShuyanStoryTeller
    @ShuyanStoryTeller 8 років тому +14

    the clearest demonstration. I was lost in the class, but after watching your videos, I understand.
    Thank you so much.

  • @HristoMitev123
    @HristoMitev123 7 років тому +5

    When it comes to calculus revision - there is no one better. Thanks a lot for the help friend.

  • @thunayyanhussam713
    @thunayyanhussam713 5 років тому +4

    Your way of teaching is like you're babysitting a math student. I love it!

  • @sano0311
    @sano0311 13 років тому

    I was loosing my mind to understand how to get shell radius but after spending 5 min watching this video everything became crystal clear. Thanks man.

  • @aznboigotzfire
    @aznboigotzfire 13 років тому

    spent hours on my homework and kept getting the wrong answers, watched this video, and then BAM! i started to get all the right answers. You are the man

  • @SZJerkXVI
    @SZJerkXVI 10 років тому +2

    Ahhh.... The beauty of understanding math.
    Thank very much you man.
    You're even the first channel I subscribed to.
    Now... numberphile and minutephysics...

  • @tahirrazzaq9494
    @tahirrazzaq9494 11 років тому

    You sir, are my hero!!! My teacher doesn't know how explain anything, so I watch your videos instead! You understand that just because you understand it doesn't mean we do, so you actually explain it, unlike my professor! He thinks because he's a know-it-all, we should be too, but we're not! So thank you so, so much!!

  • @phalgunkrishna2467
    @phalgunkrishna2467 8 років тому +9

    You have no idea how much this helped me

    • @modelaircraft12
      @modelaircraft12 8 років тому

      +Phalgun Krishna they are academics, all they care about is their research and their job. Some of them do not have the gift of teaching. therefore, professors are not hired for their teaching abilities but for research at a university.
      Some professors on the other hand, have the teaching ability and we are truly blessed when we have them :D

    • @phalgunkrishna2467
      @phalgunkrishna2467 8 років тому +1

      +franco diaz thanks, but I'm in high school. I'll definitely keep that in mind though next year.

    • @stylingandfitnessingwithty2713
      @stylingandfitnessingwithty2713 3 роки тому

      @@phalgunkrishna2467 how was campus?😅

  • @americanelephant8740
    @americanelephant8740 6 років тому +1

    I forgot how to do this after learning it in class in a 90 min lecture, I remembered within 6 min of your video. May God Bless you.

  • @dragikrase974
    @dragikrase974 7 років тому +1

    Dude I have been watching videos trying to understand this for 4 hours and you freaking saved my life

  • @immaculatepercepti0n
    @immaculatepercepti0n 11 років тому

    I'm a tutor myself, and I just wanted to say you're a good teacher man. Thanks for your awesome vids and well spoken explanations/instructions.

  • @Alain0775
    @Alain0775 15 років тому

    From the bottom of my heart thank you very much. It turns out that the way you explain makes things easier to me.

  • @B.A.Gondal
    @B.A.Gondal 10 років тому +55

    Rotating About Y-axis --> Cylindrical Shells Method Wins
    Rotating About X-axis --> Disk/Washer Method Wins

    • @crazylazy007
      @crazylazy007 10 років тому +2

      Just checking but is this due to the fact that you don't have to convert the y= x equations to x= y form or something else?

    • @B.A.Gondal
      @B.A.Gondal 10 років тому +2

      crazylazy007 yup, you are right. That's the reason. But sometimes in very rare cases, it depends on the equation too like sometimes shell method might simplify things when rotating about x axis....but in general ya...its gud to use as mentioned above

    • @hassonal-mu2524
      @hassonal-mu2524 10 років тому +1

      crazylazy007 when the problem you trying to solve is in the x-axis you will have to convert the y=x to x=y

    • @ryantran4542
      @ryantran4542 6 років тому

      in the last example when it rotating about y=-3 . i use disk/washer and it shows a different answer. idk why ?

    • @chemist7908
      @chemist7908 5 років тому

      Geez thank you for this. It actually makes sense coming from another

  • @xasma.x1786
    @xasma.x1786 4 роки тому

    words can't describe how much thankful I am for your videos.

  • @leeadnegri8662
    @leeadnegri8662 10 років тому +5

    You are a great teacher. I wish your were my Calc 2 professor!

  • @astickler5
    @astickler5 11 років тому

    Thank you for telling me what I NEED to know and not all That other theory garbage my teacher goes into. U have the most helpful math vids on youtube, and for that, I thank you.

  • @shaikhrezwanrafidahmad6771
    @shaikhrezwanrafidahmad6771 7 років тому

    Tomorrow is my semester's mid. I've been browsing your videos the last 1 hour about the trig identities/Volumes/Areas and if I do pass tomorrow it'll be because of you. You are a life saver. What is even more surprising is that we spend thousands of bucks on professors which barely could make math interesting. Though this video is about 10 years old, but you are still a legend. Keep up the good work, fam. (Y) May God Bless you.

  • @adrian0120
    @adrian0120 13 років тому

    you are the best. seriously. Such a life saver. My prof does not make sense but you just made it so easy in 20 minutes THANKS SO MUCH!

  • @mzadreexs
    @mzadreexs 13 років тому

    you are a life savior! i always go on your page when i need help with my calculus. thanks so much!

  • @larrycole7796
    @larrycole7796 4 роки тому +1

    In 100 years, when youtube is gone and the internet is replaced by virtual reality, struggling calc students are still going to be watching this video. Thanks Patrick!

  • @victor54112
    @victor54112 10 років тому

    I dont even know why i have lectures, you make calculus so much easier to comprehend, THANKS SO MUCH!

  • @didsomebodysayme
    @didsomebodysayme 11 років тому

    you are fantastic, thank you so much! my teacher only gave examples involving rotating around the x and y axis only so i had no idea how to go about revolving other axis's and how to deal with other stuff you addressed, thanks !!!

  • @joshuaoladiti
    @joshuaoladiti 14 років тому

    your teaching was down to earth, you are gifted to teach. may God continue to increase your knowledge of the subject. i say amen to it.

  • @jurrytaalib-deen7146
    @jurrytaalib-deen7146 2 роки тому

    Thank you so much for this video. You have no idea how long it has taken me to understand this. This is my third time taking calc 2 and third time is a charm because of you. I have understood everything in calc 2 except the volumes, and areas. Your videos are helping me get my degree.

  • @rolabijou1664
    @rolabijou1664 8 років тому +1

    Saved my Life!! Craming for a calculus midterm and was so lost.

  • @suhaibalbulushi2956
    @suhaibalbulushi2956 11 років тому

    you are one of the best teachers I have ever seen in Calculus. always making my life with the Math in the university much easier, THANKS A LOT ..

  • @bhujwalaali
    @bhujwalaali 13 років тому

    I didn't know anything before this, (missed a week of class) your vid is a life saver.

  • @AmberinTrees
    @AmberinTrees 14 років тому

    Thank you so much! I was feeling really terrible, because I couldn't understand, but you make it seem so easy!!!

  • @codezier2738
    @codezier2738 4 роки тому

    The BEST video out here on Cylindrical shells includes all possible cases. Amazing thank you so much!

  • @BackfallGenius
    @BackfallGenius 15 років тому

    You've got one of the neatest handwriting I've ever seen, lol.
    And thanks a ton!! This way of remembering the formula as "shell radius" and "shell height" helps a lot more than the way our teacher taught us (p(y) and h(y)...then the outer/inner difference is w, you do w/2 and it got too confusing). this is plain and simple. Ty again!! :D

  • @amrichbiatch
    @amrichbiatch 14 років тому

    dude by far .......... the easiest guy to understand thankks a lot ....

  • @OnlyHiraeth
    @OnlyHiraeth 10 років тому

    Wow! Thanks, patrickJMT ! I remember learning this during my lecture and the prof was trying to explain this but it only made things worse. Came home thinking I was going to fail the exam but then I came across your videos. You're a life saver :) Thank you once again :)

  • @billma12345
    @billma12345 11 років тому

    you're so good at teaching, that i am able to explain this stuff to other people. your teaching is contagious

  • @macyzoyaf5728
    @macyzoyaf5728 10 років тому +1

    You are so much smarter and better at teaching than my professor! I wish you were my professor!!!!!

  • @hellacencal
    @hellacencal 12 років тому

    Wow, the last 2-3 weeks of calc have been like sitting through a Chinese class. These last 3 days of watching your videos have translated all that into English haha, I just wish I had stumbled upon your videos about a week ago, I'd be a lot more prepared for my final. Thanks for what you do, it is greatly needed and appreciated.

  • @ashleygonzalez941
    @ashleygonzalez941 10 років тому

    This video was really helpful. It really explained how to solve for volume. I get alot of help from my teacher but sometimes i need help when im notbin her class and this video really helped

  • @TheCJOHNSON93
    @TheCJOHNSON93 12 років тому

    My life wouldn't be complete without you!

  • @md.rezwanulhaque4710
    @md.rezwanulhaque4710 11 років тому

    Awesome tutorial ---easy to understand and easy to remember ---better than my class teacher

  • @KardOfHeart
    @KardOfHeart 13 років тому

    Your handwriting is just beautiful... It literally brought tears to my eyes!

  • @ponderingpossumable
    @ponderingpossumable 11 років тому

    I LOVE you. I usually hate math because I do not understand it. I love math now. I am actually enjoying calculus so much just because your videos actually get me to understand it. And these volume revolutions have SO MANY REAL LIFE APPLICATIONS. CALCULUS IS SO HANDY :D Thank you for showing me the wonders of mathematics! :P

  • @sulmazz
    @sulmazz 12 років тому

    I have A calc exam today and my only hope for passing is your videos

  • @1mathfan
    @1mathfan 12 років тому

    Thank you very much for all of your videos. I just made a small donation on your website and want to encourage others to do so. Tutoring at this level would be VERY expensive!

  • @nicholasaguirre8764
    @nicholasaguirre8764 3 роки тому

    great thorough video that covers multiple situations. Much appreciated!

  • @dmsfid7205
    @dmsfid7205 15 років тому

    never had this clear explanation ever!
    I've fallen in love with your voice

  • @WhiteWidow08
    @WhiteWidow08 11 років тому

    THANK YOU!!!!!!!!!!!!
    Wow I have watched at least 15 of your videos already, great job!
    I need to be spoon fed math to learn most effectively. I wish I had known about you for calc I.

  • @nonichan8829
    @nonichan8829 7 років тому

    your way of explaining is just so fantastic and easy to understand and even memorize , thank you so much

  • @mikail511
    @mikail511 11 років тому

    You are the reason I will be passing Calc 2. Thank you for your kickass explanation that does not go into unnecessary theory like my professor!

  • @kchunielal
    @kchunielal 13 років тому

    thank u so much for posting this video. it helped me a a lot. there were some things my professor wasn't so clear on but now i get it. thanks

  • @tanim80
    @tanim80 14 років тому

    Dude you are the man. I didn't understand a thing before I watched this. Thank you!

  • @NateTheGreat555
    @NateTheGreat555 13 років тому

    Freaking fantastic. You are a life saver. I was so confused by all of the different methods. you ROCK.

  • @crystalfaqih9127
    @crystalfaqih9127 10 років тому

    Have been watching your videos my entire way through calculus. Thanks you really help!

  • @nishishukla1390
    @nishishukla1390 10 років тому

    Cylindrical shells apparently aren't even that hard. When my professor taught them, I thought I'd never understand! Wow I think you will be the reason for my passing this class. Please come teach at NIU. Thank you for your videos!! :)

  • @12davm
    @12davm 11 років тому

    i learned so much more about this chapter in here than my calc 2 class. thanks man

  • @Chavostyle31
    @Chavostyle31 15 років тому

    Quiz in 4 and a half hours... and i feel pretty confident now... nice videos...

  • @TheKunovic
    @TheKunovic 12 років тому

    greetings from the university of cape town, south africa. Your vids make James Stewarts calculus series irrelevant. You are boss comrade!

  • @sarakitdotcom
    @sarakitdotcom 13 років тому

    Wish I would've seen this months ago! If I pass my calc class, it's gonna be thanks to you! Thanks for all the vids.

  • @ZRogers91
    @ZRogers91 11 років тому

    Absolutely brilliant. Couldn't get why the shell radius was just "x" or just "y" and how to get to other revolving lines... thanks. I will remember why it works and not just slap it together because i didn't understand the concept for my math final tomorrow. Thanks!

  • @alfonsoruize
    @alfonsoruize 15 років тому

    hey man thank you so much and thank god your calc teacher haha im having mi final exam tomorrow, and i never got 2 understand this during the semester and i learned it on you tube!!!! thnks so much

  • @hash_caul976
    @hash_caul976 5 років тому

    What a teacher you are i have never seen I like it sir your this lecture
    This lecture more useful for me for exam point of view

  • @patrickjmt
    @patrickjmt  14 років тому

    @PhxPride1 it comes from the formula for the circumference of a circle

  • @brianschermerhorn7294
    @brianschermerhorn7294 10 років тому

    great video man. Thanks for doing the multiple examples. Especially the ones with the different "about x" and "about y" lines. I also liked how you did the (shell radius) * (shell height) thing. You don't know how long I spent studying the book to no avail and I finally came across your video. I'm doing a 1 block summer Calc 1 class and I don't have time to waste and this saved me. Thanks

  • @GeekJonesey
    @GeekJonesey 13 років тому

    was confused. now. everything is clear. YOU DA MAN!

  • @picsparks
    @picsparks 15 років тому

    your calc explanations are amazing. Simple and to the point. If only u did physics. My teacher isnt the greatest at explaining things.

  • @vacsealed1986
    @vacsealed1986 11 років тому

    i never go to calc lectures anymore I just watch patrickJMT and get enlightened

  • @EmperorBuggy
    @EmperorBuggy 12 років тому

    You are the most amazing man on the earth. Thank you so much, my prof did NOT explain this very well!

  • @belhdawa
    @belhdawa 11 років тому

    Finally , I understand the volumes by integrating , thanks sir

  • @ren2293
    @ren2293 12 років тому

    you sir, have a Gift. God bless you man, you have basically saved me from the horrors of my midterm! and everything else :)

  • @patrickjmt
    @patrickjmt  12 років тому

    @titenite88 happy i could help! come back any time

  • @toddj.2
    @toddj.2 5 років тому

    These volumes of revolution videos are great, like all the others. Great to review for an exam.

  • @himomimfamous
    @himomimfamous 7 років тому +2

    So a general rule of thumb is to express the functions in terms of y if rotating about the y-axis and express functions in terms of x if rotating about the x-axis? Is this the opposite of the disk/washer method?

  • @sarmason10
    @sarmason10 11 років тому

    i always recommend you to my classmates! you make calc so much simpler, thank you

  • @bavl1994
    @bavl1994 12 років тому

    I have to say, you are really great. I thank you so much for all of your videos!!!

  • @user-sq1yl5no2j
    @user-sq1yl5no2j 11 років тому

    This is very very useful.I asked my maths teacher to explain it to me about 5 times,but i still dont get it. Your x and y-axis consideration is very helpful,also the formula with radius and height is easy to remember.thank you very much

  • @patrickjmt
    @patrickjmt  12 років тому

    yea, some of the early videos had some audio issues! sorry, only a few do this!

  • @loganfisher3777
    @loganfisher3777 10 років тому

    Once again, Patrick, you come through and save the day. This video helped me A LOT to understand shells. Thanks SO MUCH! :D

  • @patrickjmt
    @patrickjmt  14 років тому

    @AmberinTrees glad it helps!!

  • @omegapolar1355
    @omegapolar1355 4 роки тому +1

    Amazing explanation THANK YOU

  • @ZAGGNUT1
    @ZAGGNUT1 11 років тому

    great stuff.; really nice to see the Shell Radius explained.

  • @youngblack4591
    @youngblack4591 8 років тому +8

    Thanks... I was having a hard time finding the radius but i am already ok

  • @madigrandaw299
    @madigrandaw299 10 років тому

    Ahhhhh THANK YOU SO MUCH. You saved me for my test today. I wish my teacher taught like you.

  • @RodesLaw
    @RodesLaw 9 років тому +1

    Just tried this on the washers and disks section and it did not work for those. When it is about one of the axis, we keep useing x or y for shell radius right? thats the only possible place of error I can think of.

  • @thatharleyone
    @thatharleyone 12 років тому

    thank you so much! you explained it so much better then my 'phD prof'.. A+ here I come! :)

  • @Sharpryno
    @Sharpryno 12 років тому

    @edwardnese two functions intersect when they are equal. So set the equal to each other.

  • @andyplace
    @andyplace 13 років тому

    Best teacher I've ever had!!!

  • @Yancham
    @Yancham 7 років тому

    You deserve way more than 683k subs. My one regret is I can't like this video more than once.

  • @WowhesNeat
    @WowhesNeat 13 років тому

    You broke it down nicely, thanks!

  • @patrickjmt
    @patrickjmt  12 років тому

    it usually just comes down to finding points of intersection of the graphs

  • @Mr98supra
    @Mr98supra 13 років тому

    man, if u taught in my university.. then id major in math! keep up the good work :)

  • @annaa3894
    @annaa3894 11 років тому

    you are such a life saver :D thank God for your videos, otherwise I would be so screwed!!!

  • @FashionZombies27
    @FashionZombies27 11 років тому

    You sir, are a genius. You amaze me with your mathematical capabilities. :)

  • @POTATOWASHERE
    @POTATOWASHERE 11 років тому

    thaaaankkkkk youuu. 10x better then my prof haha. This is so much easier then what i thought it was

  • @gendrygaming9062
    @gendrygaming9062 8 років тому +1

    hey +patrickJMT! do you have any videos tackling on the topic of the centroids of solids of revolution?? BTW, your vids always help me pass my subjects.