Disc/Washer Method vs. Shell Method (rotated about different lines)

[@blackpenredpen]

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

[@al-quran9845]

This is not a difficult questions...I know better then you

[@tanOcotO]

@@al-quran9845 No, it doesn't work that way... stop saying this that's nonsense.

[@angelmendez-rivera351]

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.

[@chiragmantri4947]

CAN U DO WITH X=3 ALSO??

[@JB-ym4up]

Where's the polar rotation ?

[@rockyboy5545]

You sign up to a college only to learn it from KZbin. It makes sense. Thank you.

[@raptorgod77]

I’ll be doing the same

[@78anurag]

Wait you learn this in college isn't this a high school course?

[@jamesarnold3286]

@@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

[@78anurag]

@@jamesarnold3286 I learnt this in Calc 1

[@brucezhang4912]

fuck me too and im doing that 2am :)

[@alanparker9608]

I love how passionate he is when he’s doing maths

[@malane8541]

Ik it’s making me happy how happy he is

[@jackkaczmarski]

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.

[@corycooper6765]

ochem did

[@orcathewanderingmammal4101]

Theyre goats

[@Josh-dp6iu]

This is the only person who’s even come close to being able to explain shell method in an understandable way

[@josueolivos3783]

can we appreciate how flawlessly he switches between black, red and blue expos to make it clear to the viewers where each term is coming from??? thanks my guy!

[@maybritSortiz28]

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!

[@blackpenredpen]

I am glad to hear. Cheers!!

[@panostriantaphillou766]

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)

[@blackpenredpen]

Panos Triantaphillou omg, thank you! I always thought it as the washing machine washer lol.

[@alexdemoura9972]

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?

[@gianlucacastro5281]

@@alexdemoura9972 It makes a lot of sense, must be because of this.

[@christianhaynes7596]

I actually laughed out loud when he said washing machine, i thought he was joking lol

[@exequieldelantar9641]

May I ask.. Is circular ring method and washer the same?..

[@joabnyabuto6041]

this man just taught me three weeks' worth of class in under an hour. That's crazy

[@takeshisatou2371]

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.)

[@philrunninger2359]

Great video! I love all the KZbinrs 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.

[@blackpenredpen]

Omg, that washer?! I always thought that as the washing machine washer lol

[@Theonlyway1445]

If this guy didn’t exists, I would fail all of my calculus courses.

[@lapislazulilapis]

haha

[@Atomic_Mushroom]

free Israel

[@hazemalsabagh7855]

I really appreciate that you dive deep into simple questions to ensure the fundamental understanding of the topic.

[@tanOcotO]

Yes, thank you, we skipped all of this because of the pandemic in my calc class

[@sukaygisiz8052]

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.

[@AustinHoelscher]

Hands down best video about this on KZbin. Subbed! :)

[@shartypants1234]

I have my calc final tomorrow and have spent the past week trying to understand the shell method to no avail before I found this video. you made it so easy to understand. thank you for posting lessons like this and helping us struggling students!!

[@ld-vt9sn]

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!

[@Alex-bc3tt]

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 🙏🙏🙏

[@elias78910]

Thank you. It really helped me

[@DavGre]

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.

[@andrewa7952]

A great help visualizing when online classes don't do nothing!

[@silasjoao8953]

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

[@panovitch]

kkkkkkk br realmente ta em todo lugar

[@rafaelb.333]

Acompanho esse canal desde que comecei a estudar matemática direito hue

[@andrewcarvalho9158]

Isso aí é cálculo 2?

[@panovitch]

@@andrewcarvalho9158 sim mano, calculo de volume de solidos usando integral

[@LuizFernando23250]

@@andrewcarvalho9158 Eu vi em cálculo 1 mesmo

[@banthatiwisdom6783]

Thank you for your time. If it wasn't you I would have not understood all these. *Highly appreciated from South Africa*

[@incognito6751]

Ever since The Organic Chemistry Tutor started paywalling his videos, I've been struggling in math. Thank you for this.

[@sihlesamukele4556]

i thought i would never find someone like him, but guess what i just found the one BLACKPENREDPEN

[@marcusmoulia639]

you can really see how passionate he is for teaching math through this video. great work, keep it up!!

[@blackpenredpen]

I appreciate that!

[@ladyeillie671]

For someone who has been confused between the shell and disk/washer methods, this was very helpful for comparison.

[@epictrooper2568]

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!

[@milk6489]

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

[@fkncompton7124]

Learned this like 2 years ago and watched the whole thing anyways for a refresher lol good video

[@Sg190th]

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.

[@rachelkiss302]

God Bless his soul. He just saved me for my test tomorrow. Thank you for your service sir.

[@narutofan2010san]

You are a king! You explained chapter 7.2 of the Stewart Calculus textbook in 30 mins. Thank you sir!

[@jamerthegamer13]

9:30 man i never thought about them as two different disk methods, that’s so much easier thank you!

[@maggiedriggs9642]

he somehow made me smile doing math! such a kind and clear teacher, thank you for these lessons!

[@blackpenredpen]

😃

[@simatwokirwa4500]

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.

[@xgyra]

I had the weird sense that I should study ahead over the weekend and ended up getting sick on the first day of this week. The notes I took over this video are going to carry me. 🙏 (Thank you! This was an incredible guide.)

[@zunairarahat]

I blanked out for 2 hours trying to learn this in class and fully understood you in less time. Thank you so much!

[@michaela6396]

One of the best instructors I have had help me practice Calculus. Thank you for your videos

[@aftabafii.]

Clean explained everything without any confusion give me a lot of concept without questioning answering

[@chasemckinley2]

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!

[@marazali1816]

this has been a great help to actually understand the concept, i am very thankful for this video my good sir

[@105-ssaiswaroopa9]

I am just getting interest on the subject, just by seeing him...what ah positivity his face has!!!! Wow!!!

[@bobbob3659]

Mr.blackpenredpen you are the goat!!!!!!!!!!!!!!!!!!!!!!!

[@faroseflinch4053]

I'm having calculus test tomorrow,this help more than 2 hr lectures,wish me luck

[@BelindaCho]

love u broooo, youre strongest math teacher Ive ever seen

[@CarlosMolahlehi]

you have my respect sir. i now have the full understanding of shell and washer method because of you.all thanks to you sir

[@justinhastie3851]

I really appreciate your enthusiasm. You breaking it down like this really shows how easy it is. Thank you so much :)

[@makke2170]

This is probably one of the best, if not the best, ways to learn maths. Fantastic video!!

[@blackpenredpen]

Glad to hear. Thanks.

[@TDL0347]

I were studen 2000 years . But you are my idol

[@onion-brawlstars9792]

this video integrates everything you need to know to ace solid of revolution

[@xioxy7193]

I have a test about this today. The video recomendation was brilliant i think im ready now for it. Thank you Blackpenredpen.

[@thekishorkhairnar]

Excellent video... Perfect explanation... Love from India 🇮🇳 ❤️

[@BalaMurugan-hk2gd]

You made me so much happy. I could not describe in words because my English is so poor. Thank you dude.

[@Nigixmitama]

You just saved me 25% of my whole semester, thank you!!

[@acoustickunal578]

this video helped me a lot today was my class and hardly understand anything you helped me thanks!!

[@annierod]

I was able to understand the concept thanks to you 🙏

[@gilbertley1309]

One of his best videos for sure!

[@geoffreybwalley6498]

Wonderful!! I was struggling to understand the topic But you make it easy, I tackle questions from any angle Your explanation is Amazing .

[@blackpenredpen]

Thank you. I am glad to help.

[@gianninagarcia6842]

YOU JUST SAVED ME! ALL HAIL!

[@kenokai.]

Exam in like 2 hours and I swear I have watched this video along with a few other of his like at least 3 times each and It has really helped me get the logic down. Fingers crossed I can apply the logic I learned on the exam

[@blackpenredpen]

Best of luck!!

[@eir6791]

howd it go i have an exam in 35.5 hours 😭

[@kenokai.]

@@eir6791 went well, 26/30! goodluck!

[@shemayrays7632]

Thank you, I learned a lot. Keep up the good work. Support here from the Philippines.

[@pr0dsatya]

When I get my degree and start earning a salary I will certainly be donating to this channel

[@blackpenredpen]

That’s very nice of you. Thank you. 😃

[@aliatejeda6210]

you just saved my math grade! THANK YOU!!!

[@Araxatu]

I learned more about calculus in this video than I learned in college in one year

[@yeellee4780]

Just in time for my AP calc exam. Thank you very much

[@isaiahlobert7843]

You are a life saver my man!

[@enqiwu5307]

Thank you so much for creating these content. I have been failing my Calc BC class until I watched your videos :)

[@FelixTheForgotten]

"Just like washing machine, Washer has hole in the middle." - BlackPenRedPen - 2020

[@ezachle]

this is so much more clearer than what my teacher had taught me. thank you!

[@biggerthaninfinity7604]

Here is one guy who makes math fun

[@samuellim4956]

thank you for helping me! You are better than my prof!!!!!!!!!!!!!!!!!!!!!!

[@kenpachicg]

This just might be what I needed for my Calc 2 test today

[@jonascaburnay4839]

i was having a hard time reviewing my instructor's pdf, thank you for this!~

[@rada4917]

seriously ur videos help so much

[@brownwater6212]

I'm not in Calculus yet, but I love watching your videos regardless.

[@austin7843]

You deserve the Presidential Medal of Freedom.

[@semajzomollo3286]

you were oddly entertaining and instructive I learned a lot thank you

[@allaylu2802]

This was a very well explained video. I was not able to do it on my own until this video.

[@alexdarafeev809]

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.

[@Ducky_shades]

For love of calculus keep on writing my blackpen and solving my redpen

[@juliadeluis1132]

Thank you for explaining this!!

[@collinnovak8914]

this man draws better than my professor at Purdue

[@stimulus7222]

Hahha. I will come back and verify this comment after next fall😎👏

[@Anna-qp1fi]

Man, I really love this guy!

[@rosendjavera7734]

You are such a genius ,i didnt this topic was this simple❤🙌

[@YaraHMY]

Thank you so much, the book explanation is difficult to grasp.

[@goodmen5527]

It’s so weird to go back to the stuff that you loved so much to end up forgetting the reasoning behind it

[@suteguma0]

bro teaches me more than my Calculus class 😭

[@nunoskid153]

YOURE THE BESTTTT THANK YOUUUU FINALLY SOMEBODY DID THIS RIGHT

[@edisonflores6486]

4 years in college and this is the 1st time I understand disk washer method and shell method.

[@mrsamiam7872]

Math exam tomorrow thank you so much bro 🙏

[@hillsidebilly4649]

This video is incredibly good.

[@akolangto8225]

Thank you so much sir! This is what im looking for, explaining the concept and derivation of the formulas especially area and volume . From the philippines

[@potatoeater8014]

didnt understand disks+washers until this video, thank you bprp :OO

[@MFRSIAM]

this video fucking save my life , so many thanks man a truly lifesaver.

[@comingshoon2717]

Este video debería llamarse “lo que tu profesor de cálculo 2 no te enseña”... lamentable .... Gracias maestro BPRP💪

[@iris-hb9qs]

this video is very useful and helped me a lot! wishing the best for you 🥰🙏❤

[@kennymccormick6846]

Holy shit, i think this video just saved me. Thank you!

[@kuppuswamyravi5714]

Very good presentation I understood very well

[@purplelala2]

Great video!! Helped me figure out how to set up my equations

[@blackpenredpen]

Glad it helped!

[@edu10th47]

21:30 why do you use the area of a circle (xrsquared) times its thickness for the washer method but then you use the circumference of a circle times the height and the thickness for the shell method? Why not use area for both of them?

[@sethJeon]

this channel should be blackbluepen