Disc/Washer Method vs. Shell Method (rotated about different lines)
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- Опубликовано: 21 авг 2024
- Volume of Solid of Revolution rotated about different lines. Disc method vs. shell method for calculus 1 or AP calculus students.
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Hope this helps with your calculus 1 or AP calc
Time stamps:
a) area of the region, both vertical and horizontal rectangles 0:06
b) rotate about x-axis, 5:58
c) rotate about y-axis,15:16
d) rotate about x=5, 21:51
e) rotate about y=3, 30:56
This is not a difficult questions...I know better then you
@@al-quran9845 No, it doesn't work that way... stop saying this that's nonsense.
Mathematician Way Don't be an asshole. This isn't about whether it's easy or not. It's a video meant to help calculus students who are struggling, it's obviously not meant for people such as yourself.
CAN U DO WITH X=3 ALSO??
Where's the polar rotation ?
You sign up to a college only to learn it from RUclips. It makes sense. Thank you.
I’ll be doing the same
Wait you learn this in college isn't this a high school course?
@@78anurag this subject is generally learned at either the end of Calc 1 or beginning of Calc 2, or both, but this just depends on what calc 1 and 2 course you took. But people still take calc 1 in college, so it would make sense either way to be learning this in college
@@jamesarnold3286 I learnt this in Calc 1
fuck me too and im doing that 2am :)
I love how passionate he is when he’s doing maths
Ik it’s making me happy how happy he is
This man may have taken the GOAT throne. No shade to The OChem Tutor or Sal Khan (they're both great and have done a lot for me), but NO ONE has been able to teach me washer method until this man. Thank you Blackpenredpen.
ochem did
Theyre goats
This is the only person who’s even come close to being able to explain shell method in an understandable way
A washer is a thin plate with a hole (typically in the middle) that is normally used to distribute the load of a threaded fastener, such as a bolt or nut.
en.wikipedia.org/wiki/Washer_(hardware)
Panos Triantaphillou omg, thank you! I always thought it as the washing machine washer lol.
Yes, _"Washer method"_ is not after someone's name. But we may suppose it is *not* related to _"washing machine"_ as in _"washer"_ , a person or device that washes something, and as in _"wash"_ verb, clean with water and, typically, soap or detergent.
It is more related to _"washer"_ , a *flat ring* fixed under a nut or the head of a bolt to spread the pressure when tightened or between two joining surfaces, since we subtract a smaller disc from a bigger disc, we got a *washer disc* or flat ring. Do you gents agree?
@@alexdemoura9972 It makes a lot of sense, must be because of this.
I actually laughed out loud when he said washing machine, i thought he was joking lol
May I ask.. Is circular ring method and washer the same?..
If this guy didn’t exists, I would fail all of my calculus courses.
haha
free Israel
I cannot express enough my gratitude for your videos! I struggled to conceptualize washers/disks and shells, but with your thorough explanations, I could tackle these questions with ease. Thank you!
I am glad to hear. Cheers!!
this man just taught me three weeks' worth of class in under an hour. That's crazy
3 weeks? my university taught us this in less than a week and expect us to be able to understand it lol. My university's curriculum is insane. (Not gonna expose my university, but it's 1 of the top 5 universities in asia as of 2024.)
Great video! I love all the RUclipsrs making math more easily understood. Just a point of clarification... "Washer" refers to a fastener used in combination with a bolt and nut, not a washing machine.
Omg, that washer?!
I always thought that as the washing machine washer lol
For someone who has been confused between the shell and disk/washer methods, this was very helpful for comparison.
I really appreciate that you dive deep into simple questions to ensure the fundamental understanding of the topic.
Ever since The Organic Chemistry Tutor started paywalling his videos, I've been struggling in math. Thank you for this.
i thought i would never find someone like him, but guess what i just found the one BLACKPENREDPEN
Hands down best video about this on RUclips.
Subbed! :)
man i'm brazilian and my classes were suspended due to the covid-19 pandemic, your classes have helped me a lot, here we see this in calculus 2 continue with this incredible work and may god bless you
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Acompanho esse canal desde que comecei a estudar matemática direito hue
Isso aí é cálculo 2?
@@andrewcarvalho9158 sim mano, calculo de volume de solidos usando integral
@@andrewcarvalho9158 Eu vi em cálculo 1 mesmo
I can't believe that a few years ago I watched your channel, and I had no clue what all those hieroglyphs were on the whiteboard, And now I'm watching your videos for an explanation! keep up the amazing work, I love your videos! thanks!
Yes, thank you, we skipped all of this because of the pandemic in my calc class
This video needs to be the first thing lectures show to their students 🤣🤣🤣Very much descriptive and straight to the point, it even helps train the mind how to visualize the solids of revolution. Keep up the good work 🙏🙏🙏
i've never commented on a youtube video before, but dude i was depressed at my final exam week and you made my day with your smile. thank you! keep doing it. you are amazing at your job.
A great help visualizing when online classes don't do nothing!
Learned this like 2 years ago and watched the whole thing anyways for a refresher lol good video
Haha same. I didn't get a full grasp of learning this but it was really fun. Everything in previous math used for calculus. Can't believe I thought it was generally difficult.
Thank you for using the same two functions for the different examples, I hate when some videos try to explain the different rotations but pick a bunch of different functions for each method and rotation, this makes it crystal clear to understand the fundamental concepts without having to rewatch or pause a lot.
you can really see how passionate he is for teaching math through this video. great work, keep it up!!
I appreciate that!
You made this so easy to understand. Up until this point I did not really understand these methods at all but now I actually understand what I'm doing. Thanks!
God Bless his soul. He just saved me for my test tomorrow. Thank you for your service sir.
he somehow made me smile doing math! such a kind and clear teacher, thank you for these lessons!
😃
Thank you for your time. If it wasn't you I would have not understood all these. *Highly appreciated from South Africa*
9:30 man i never thought about them as two different
disk methods, that’s so much easier thank you!
bro you dont understand how much i love your explaining and the way you teach, ive never thought id give props to a tutor on youtube but you are levels beyond anyone else on youtube teaching
You are a king! You explained chapter 7.2 of the Stewart Calculus textbook in 30 mins. Thank you sir!
I love you, seriously.
You've helped me so much through college
this video integrates everything you need to know to ace solid of revolution
I'm blown away that this much visual clarity on volumes of solids of revolution came from a video without some 3D graphics computer program involved. Loved the vid/thanks for making this!
this man draws better than my professor at Purdue
Hahha. I will come back and verify this comment after next fall😎👏
This is probably one of the best, if not the best, ways to learn maths. Fantastic video!!
Glad to hear. Thanks.
this has been a great help to actually understand the concept, i am very thankful for this video my good sir
I blanked out for 2 hours trying to learn this in class and fully understood you in less time. Thank you so much!
Clean explained everything without any confusion give me a lot of concept without questioning answering
Mr.blackpenredpen you are the goat!!!!!!!!!!!!!!!!!!!!!!!
One of the best instructors I have had help me practice Calculus. Thank you for your videos
Here is one guy who makes math fun
I have a test about this today. The video recomendation was brilliant i think im ready now for it. Thank you Blackpenredpen.
I am just getting interest on the subject, just by seeing him...what ah positivity his face has!!!! Wow!!!
4 years in college and this is the 1st time I understand disk washer method and shell method.
YOU JUST SAVED ME! ALL HAIL!
You made me so much happy. I could not describe in words because my English is so poor. Thank you dude.
I really appreciate your enthusiasm. You breaking it down like this really shows how easy it is. Thank you so much :)
Comment on 10:44 - Washer method because the shapes do not look like wash-machine BUT because the outer shaper/graph relates to WASHER y = root-x and the inner shape y = half-x relates to BOLT that goes into washer or ring. .. .very good intuition on finding area / volumes under curves using integration. .. good job.
When I get my degree and start earning a salary I will certainly be donating to this channel
That’s very nice of you. Thank you. 😃
you just saved my math grade! THANK YOU!!!
Wonderful!! I was struggling to understand the topic
But you make it easy, I tackle questions from any angle
Your explanation is Amazing .
Thank you. I am glad to help.
I'm having calculus test tomorrow,this help more than 2 hr lectures,wish me luck
I learned more about calculus in this video than I learned in college in one year
you have my respect sir. i now have the full understanding of shell and washer method because of you.all thanks to you sir
I'm not in Calculus yet, but I love watching your videos regardless.
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this video helped me a lot today was my class and hardly understand anything you helped me thanks!!
I was able to understand the concept thanks to you 🙏
One of his best videos for sure!
You just saved me 25% of my whole semester, thank you!!
"Just like washing machine, Washer has hole in the middle." - BlackPenRedPen - 2020
i was having a hard time reviewing my instructor's pdf, thank you for this!~
I were studen 2000 years . But you are my idol
For love of calculus keep on writing my blackpen and solving my redpen
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Perfect explanation...
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This video is incredibly good.
Just in time for my AP calc exam. Thank you very much
It’s so weird to go back to the stuff that you loved so much to end up forgetting the reasoning behind it
You deserve the Presidential Medal of Freedom.
loved the martini glass joke lol. also, very helpful video. wish me luck on my test tmrw!! lol
this is so much more clearer than what my teacher had taught me. thank you!
didnt understand disks+washers until this video, thank you bprp :OO
Thank you so much for creating these content. I have been failing my Calc BC class until I watched your videos :)
this channel should be blackbluepen
thank you for helping me! You are better than my prof!!!!!!!!!!!!!!!!!!!!!!
This was a very well explained video. I was not able to do it on my own until this video.
If this is the hardest part of calculus, I'm golden.
Thank you. It really helped me
Este video debería llamarse “lo que tu profesor de cálculo 2 no te enseña”... lamentable .... Gracias maestro BPRP💪
YOURE THE BESTTTT THANK YOUUUU FINALLY SOMEBODY DID THIS RIGHT
Thank you for your service, good sir. You make the best videos for understanding calculus. Great teacher, you convey the info quickly and concisely enough that my attention doesn't drift lol.
Thank you, I learned a lot. Keep up the good work. Support here from the Philippines.
You are a life saver my man!
bro teaches me more than my Calculus class 😭
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thank you for this, i really couldn't get it when only reading the module
Next time please show us how to find the volume of rotation/revolution about a SLANTED LINE (like y = x/2 in this case).
Rotate the function
@@johnny3475
Right. Show us how.
How about rotating around the line y=5-2x ?
(i.e. perpendicularly intersecting y=x/2 at (2,1) )
Personally, I would just use two integrals. Integrate first with respect to y. (x/2 =< y =< sqrt(x)) and then integrate with respect to x (0 =< x =< 4)
You are such a genius ,i didnt this topic was this simple❤🙌
Math exam tomorrow thank you so much bro 🙏
Math is an integral part of my life,is is for yours?
This video being uploaded in my birthday is one of the best things that happened to me today, so yes.
Math am part of my life
math has been a great addition to my life
Yeah my life is the derivative of maths too
Maths is an interal part of my life and differentiates me from others.
Sorry if I misheard this, but you were talking of the "washing-up" kind of "washer" at one point. Just in case that's what you're trying to relate the method name to, here's Wikipedia on the nut, bolt, and washer, versionr, which fits the usage here better. en.wikipedia.org/wiki/Washer_(hardware)
I think this interpretation of the "washer" in 'washer method' would be well correct if the two integrals were fused into one, but not really when kept separate.
Holy shit, i think this video just saved me. Thank you!
the washer I think is disc cylindrical washer since it is a 3 dimensional figure.. great explainantion.. great help in times of online class where onliine modules are so difficult to understand
saved my calculus grade once again
I might be early for the video, but you are late... 2 months late, when this topic was presentend to me for the first time. As always, excelent video.
I love this guy.
Find the envelope of a straight line x/a +y/b=1 where the parameted a and b related by the equation a^n +b^n =c^n
Video so goated, enemies couldn't dislike
Thank you for explaining this!!
this video fucking save my life , so many thanks man a truly lifesaver.