Volumes of Revolution about Vertical Lines Using Washers

[@ducksoop.x]

Lately I've been getting ads for "ThatTutorGuy" while watching your videos. It's hilarious how they try to portray free videos as not being helpful. I've gotten through all my college math with your help and Paul's Notes and it didn't cost me a dime. You're way better than that tutor guy!

[@pnbmaps2286]

No, The chemistry tutor is the best there is. LOL😆😆

[@Hegeleze]

"Just to give you a basic, systematic way to set these things up." I wish all professors would take this advice. People don't need more examples, they need systematic problem solving tools to use on examples. Good video, thanks!

[@squidin9347]

16 years later and this video is STILL helping people. Thanks a bunch man!

[@patrickjmt]

happy to help :)

[@leo14992]

you making tea?

[@zain4019]

socks n sandals the sound of a chorus of kettles... and now we know the secret to Patrick's sanity while doing math all day.

[@chemlab12345678910]

Amazing video, but that background noise is killer.

[@marcomangiola9403]

Fr

[@BangMaster96]

I dont know why some people disliked your videos. But you are the best and the greatest mathematician of this Century None of my math teacher, or even the hundreds of thousands of math teachers of everyone who watches your videos can explain the hardest stuff in the easiest form possible. All hail Sir PatrikJMT The Greatest

[@taymurahmed7119]

+Sunny shah They have allergy with goods !!!

[@taymurahmed7119]

lol... ur professor is cracked... i'hv done my hole university mathematics with help of this mans video :)

[@TheFreezingTuberJosh]

Hole?? XD

[@goliathstone3110]

4:57 : Thank Goodness! After 4:59: No!

[@amandawinsor5688]

My reaction exactly!

[@goliathstone3110]

My ears felt so relieved :) But just for a second :(

[@TreasureGodsCreation]

I was like, "At last!" :P

[@ttkyle231]

Thanks for these videos, the way you explain it makes it a whole lot easier to understand. I finally get it. Such an easy concept when explained correctly.

[@WompyConk]

"A genius is someone who takes a complex thing and makes it look simple." - Robert Fanney. You Patrick, are a genius.

[@luxmartyr]

you teach the same way my lecturer teach me... except that you make it look easier 😁😁 thank you sir for your good video.

[@rajababu-bp4lx]

Excellent sirr

[@7eguegueh499]

Patrick, you are helping me with my homework. Your videos are always helpful, and I'm glad you exist. *has a lot of joy*

[@hottyJunsu]

You're such an amazing teacher!!!! I could understand so much more from your 10 min vid than my teacher for 3 hours. Thank you for helping lost kids like me.

[@jeffmarlowe2727]

You explain it soooo well. Thank you. I appreciate the explanation of the setup. The textbooks miss those steps and rush through.

[@salimrezajim527]

oh my god what I have done in the whole semester I understand the whole things in just 20 minutes ....amazing ...thanks very much magician

[@patrickjmt]

this was an earlier video... most of the sound issues have since been fixed. thanks though.

[@adil4322]

Spent two hours before trying to understand from textbook and stuff. but useless, thank you very much!

[@lauraaa2621]

you and your tea kettle out here saving lives :,)

[@Busterrhymes6]

You are the greatest! If only my professor would explain things simply like this. Thank you so much!

[@Athear.]

one of the best math teachers, if not the best.

[@patrickjmt]

thanks!

[@DROSE1DHEST23]

He uploaded it on Pie day!!!!!!!!

[@patrickjmt]

@supersal001 a large portion does actually. it is why i am going to start working full time on making videos starting next year. the ads are why the videos exist - someone has to pay for all this free stuff.

[@stitchinginthebarn8307]

Thanks! I missed a Cal2 class already and you explained it perfectly!

[@MeGustaMiRaggae]

You likely get this a lot, but you're my replacement prof from now on. You make sense and actually appear to CARE about TEACHING. Universities should hire people like you. How some of these profs get jobs in education now-a-days astounds me.

[@siscohernandez9002]

Thank you for existing !! Helped me through all my math classes i have taken in college !

[@rohangiga]

you are better then my lecturer!! love you patrick!!

[@kaileejohnson101]

You single handedly got me through calc 1-3

[@coolpig96]

Thank god that you made such videos. Without you I might be having hard time in completely understanding Washer and Cylindrical Shell Method. I can't even understand anything from my lecturer and I can easier get hold of the grip and understood every single thing you said in this all short videos you made. May god bless you sir.

[@patrickjmt]

@ICarnag3I yes, if you use shells it should be with respect to x.

[@Ali-dn9tl]

why are there 12 dislikes ? must be our calc teachers...

[@DennisAltman]

or more likely that obnoxious squealing in the bkgd?

[@patrickmoloney672]

What squealing? Just use ad-block.

[@PixelYohan]

Not that much of an obnoxious sound considering it was a video created and uploaded in 2008...

[@ayuparpe1580]

hahahhahahha wtf defenately they must be calc lecturers

[@jeffreywoelfel7876]

that high pitch noise is the best. I love your videos Patrick, and when I get money I'm going to buy you a camera. Its the least i can do for helping me pass calc.

[@dellanomike]

I was taught a different method, not the outer/inner radius thing,your method is so much better....

[@patrickjmt]

@CoconutMigrating it depends on the geometry of the region and depends on where the line is....

[@matthewfuchs5717]

your videos have helped me get through all my calc classes so far, thank you for all your help! Your videos are great but what's buzzing in the background?

[@lifelyrics5659]

Crickets

[@vincentvalbjorn]

ur the best patrick. thanks for helping me excel in calculus.

[@sibongilemakhanya5155]

I love your lessons Patrick they are really helpful 🙌🙌🙌😍😍😍

[@patrickjmt]

@ICarnag3I in this case at least

[@jdlsports94]

patrickJMT....you are the man.....respect

[@yasminhassan8220]

Damn I was 1 year old when you posted this. 2020 anyone?

[@patrickjmt]

i'm already in 2022

[@xoxomelissaabed]

Hey! Thank you SO much for your videos! They are awesome. PS: I know you don't want to go through all of the integration and algebra, but is there any way that you can add the answers at the end just so that when we finish it ourselves, we know we have reached the correct answer? Thanks!

[@ahmeddeghady4510]

been 2 years on your comment but anyways there's tons of ways you can know the correct answer, maybe symbolab or wolfram will do the job.

[@femiairboy94]

I love math, but you just make me love it more.

[@patrickjmt]

it is true, i do like teaching

[@patrickjmt]

@DonenDone10101 i do not know of a formula off the top of my head, i would have to derive one.

[@tombey12]

Thanks buddy! Learned so much from you lately

[@patrickjmt]

@ICarnag3I it depends on what method you use

[@patrickjmt]

glad i could help you out :)

[@patrickjmt]

@SirDamienQFox probably

[@mirzarameez3255]

Excellent 🤗🤗

[@akvolkswagen]

Patrick is great!

[@theforgemaster1688]

This helped so much thanks.

[@patrickjmt]

@TheAnonymousify old video, crappy mic i guess

[@Chimpalimp1001]

May I suggest using different sound recording software, or a headset mic. The feedback gets irritating. Very thorough, awesome stuff!

[@dmsfid7205]

I can't say thank you enough!

[@Smallpplwin]

Both those answers are correct !

[@govindkujur6782]

Thx a lot

[@leylasolmaz3978]

is first example washer or disk. i think disk. because function doesn't have any hole when we calculate volume. Could you answer sir? patrickJMT

[@BrownieX001]

Washers and Disks are the same. Washers/Disk are different from shell. pi(R^2-r^2) vs 2pi(shell radius)(shell height).

[@msujonbd]

Yes, 1st example is disk.

[@Jozyrose]

Thank you so much Patrick!!! =o)

[@venkatbabu186]

What is a curve. A completely broken line. What is a volume. Cluster of lines with regular breakage. Why do lines break. Because of irregular structure. What is regular. Lines with zero and one.

[@Zoeey115]

Thank alot for helping out there mate! :)

[@stevenpark6923]

Patrick, what happens when you can't find the limits of integral because when you set them equal to each other, it is hard or impossible to solve?

[@bobstanley8297]

For the last problem, if it was rotating about the x = 3 Does that mean the Outer = (3 - y)^2? Inner = (3 - y^2)^2?

[@lloveliz]

bob stanley no I don’t think so, that would be right if it was rotated about y=3. but bc it’s being rotated about x=3, its R(which is the outer radius)=(3+y)^2 and r(inner radius)=(3+y^2)^2

[@bubuA08]

finally, i get it. thanks

[@erwynesantos]

thank you :)

[@patrickjmt]

haha, not quite : ) glad it helps though!

[@jangkaenet5743]

I wonder how many papers you are using in each of your video..😁 But seriously, your videos helps a lot in my calculus class.😊

[@iluvicecream123]

I can't find the one about revolving it about the horizontal line. Help please?

[@moazelsawaf2000]

Thanks sir

[@SuperSweety1993]

thank you vary much :D u make it easy for me

[@BornInsane0]

what do u do if u are only give x axis ]

[@naba6083]

Man you're a saviour 💞

[@CoconutMigrating]

I have a question here. Wikipedia says that when the axis of revolution is not the x or y axis, you should take the (line - equation). Here you took the (line + equation). Why is this?

[@saudalbidah4660]

I love you Patrick

[@muhammadhasan4881]

since the arrows for outer and inner radius are horizontal wouldnt we want to get the x distance and not the height y?

[@lastdevil941]

Can someone please tell me why he did not use the radii difference method for the first problem?

[@BrownieX001]

because this is about washers and disks. whats radii method?

[@MultiMoe91]

hey patrick thanks for the video of Volumes of Revolution - Disk/Washers Example 1 .. i have a question which is bugging me.. in the first example you wrote its rotated in the x-axis. can't we use the formula pie intergal c to d [g(y)]^2 ? i'm kinda confused when to use it exactly thanks :)

[@bobstanley8297]

And do you mind putting the volume videos in a playlist please?

[@xxbia]

@patrickJMT I wish I could be a full time KZbinr! :) Sounds like a fun way to make a living.

[@saxboss1]

Can you just use the shell method for this?

[@saxboss1]

Specifically the problem at 7:00

[@milkcar92]

what about translating the graph to integrate it?

[@DonenDone10101]

Patrick, I'm having a dilemma finding something. All of the examples of solids of revolution involve only vertical and horizontal lines. I was wondering as to how you would go about rotating a graph about a slant line such as y=x. The only thing I can think to do is rotate the graph, before integrating, such so that the axial line becomes the x or y- axis. Is there even such a problem, or am I just searching an ignorant idea? Please help. Any help is much obliged. ^.^

[@Boot1221]

AWESOME ! ;D

[@iXtErMiNaTe]

last minute studying for this AP exam tomorrow LOL

[@matooq7432]

What if the axis of revolution in between the region?

[@ActuatedGear]

17pi/15?

[@HJ-jl5pj]

yass same

[@cmurph5039]

how do I do it if I cannot integrate the equation in terms of X. like it's too complex? does he have a video on that? that's what I get stuck on

[@leprechaun7482]

Wish you mentioned y=sqrt(x) looks same as y^2=x.

[@Spartacus_SohaR]

Thanks Patrick , I have a problem I solve it but it comes to (-) ,,,, y=(x+1)^2 , x=0 , y=0 , about y-axis , can u help me plz?

[@aboyeazin11]

sankz you, you za maaaan

[@lloveliz]

Great video but the answer is not given at the end, really wished it was so I could cross check my work

[@daminisharma6096]

Sir if we have x=-1 and we have to rotate it to x=-2 then what will we do?? Do not we have to add 1 into it but in the solution they haven't add anything.. Please explain

[@weissmann48last49]

Do one for x=-1 then x=-2 then add the 2 of them

[@user-vm3cf8cc2r]

❤

[@TennisPoet]

Hey PatrickJMT I know you have a 10 min limit and whatnot, but could you please put the answers to the problems you don't solve all the way through in the description or something? Just in case I make a stupid mistake, I'd like to catch it to make sure. The first one I got (1023pi/5) and the second one I got (17pi/15) Thanks.

[@mollyc2575]

Question. Why do we call it washers? Does it look like washing machine??

[@patrickjmt]

they are called washers as a 'washer' is a type of bolt that people use when fastening things. google 'bolt nut' and check out the images :) they look a bit like a thin metal donut. likewise the regions that get revolved would like a bit like a washer as they would be thin and have a hole in the middle :) sorry for thinking you were joking :)

[@patrickjmt]

google 'washer bolt' that is

[@mollyc2575]

Now I see! Thank you. Before you telling me this, I belived that it must be the image of washing machine whirling around as it worked. Ignorant I was.

[@ICOD73]

4:57 The Annoying Sound is finally over :) 5:00 OH WASHER! :(

[@fossilfighters101]

Oh my goodness that noise is painful.

[@JerrodVoong]

What would happen if it were rotating at x=3 instead of -3?

[@BrownieX001]

the signs would flip when inputting into formula...

[@serpensortia01]

i think you forgot to write dy in that general formula at 1: 48

[@yunfeichen9255]

really the sound was annoying to me for the first 30 seconds and then i shut it off in my head and ignored it.......

[@supersal001]

@supersal001 unless all add rev goes to patrick...come at me ads

[@IFYOUWANTITGOGETIT]

Why is there so much feedback noise?