Longer Version - Volumes using Cylindrical Shells

[TheBlazeofRazgriz]

the video is great, i just wish you would do the intergration, as some of us might not have strong intergration skills. but still an awesome video very helpful. i watch all of ur videos on any subject i have trouble with

[zeroin1330]

is the graph you were drawing even possible?

how could y=square root (x) be higher than y=x?

[SBarkerCCHS]

@zeroin1330 The values from 0 to 1 of square root of x are greater than y=x. Example: square root of x=1/4 is 1/2. For y=x, the value would be just 1/4. 1/2>1/4

However, for the interval of 1 to infinity, y=x is greater than square root of x. But because the intersections are x=0 and x=1, you take top function - bottom function to find the height. Because the values of square root of x are greater than y=x for that interval, his graph is possible.

[zippy133713]

I'm confused...how do we know which function is the radius ? i know its y here but I can't understand how its not y^2

can anyone help ease this confused mind?

[SBarkerCCHS]

@zippy133713 Unless I'm mistaken, the radius of the shell is just the distance from the shell to the axis of revolution. If you're referring to the 16:23 example, the radius from a shell to the x-axis is just y-units. Then you add the 3 units necessary to get to the y=-3 line.

Correct me if I'm wrong, but, unlike disks and washers, with shells, you do not square the radius of the cross-section. Hopefully you found this helpful. Once again, correct me if I'm wrong.

[deptload]

i just got an add at the halfway mark. wtf Youtube.

[Anity9393]

is that a leaf blower in the background?

[mistersirisaacnewton]

15:15 scared me

[vexxice]

Thank you, This will help me with my calculus Exam.

[itempus]

Thanks for the vid dude.

[titenite88]

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

[patrickJMT]

@titenite88 happy i could help! come back any time

[Withlove133]

Hey, at 9:00, if the graph was rotating about the line x= 1, would the radius be (1-x)??



[Mrjammintime1]

@Withlove133  yes

[deadend299]

are we supposed to know how to graph sin(x^2) cuz i tried it with first derivative and second derivative but it didnt work

[Angelgrrl04]

9:56 - Why is the shell radius x+4? Is it because originally x-(-4)?

Someone please let me know asap, thanks!

[hermanyulol]

@Angelgrrl04 yea its just x-(-4)

[Angelgrrl04]

@hermanyulol Okay, thank you!

[staronline1212]

@Angelgrrl04 just the absolute distance from the axis of rotation

[AliveDog]

My second time watching this video. Also the second time I had a heart attack at 15:16

[ipodvidoe]

Hello. How did you find the limits of integration for the second example at 9:00?

[chandlerstimach]

shell-parallel! thank you!

[franklinade]

amazing video i understand now easily with your methods thank you

[Merlin10108]

Anybody else see a face with one eye at 8:09 ?

[slammingsam512]

how do you know when to use cyclindrical shells or washers?

[KhaosSoulFury]

@slammingsam512 whichever you want bud

lol

[timmy11zoomsharecom]

I have 2 questions. On the first example, why do you multiply by x and f(x). Wouldn't just be f(x). Also is it possible to do the first example but revolve it about the x-axis?

[696SHANI]

@timmy11zoomsharecom In the first example 'x' is the radius, volume formula is 2pi * (radius)*(height) so in place of radius we put x..And the 2nd part i dont really get it

[timmy11zoomsharecom]

@696SHANI oh ok. Thank-you btw your math videos are very helpful

[edwardnese]

how do you find limits of integration do you set the function equal to each other or zero

[Sharpryno]

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

[Loggs777]

Could you use the disk method for the first one with sin(2x) and y=0?

[sulmazz]

I have A calc exam today and my only hope for passing is your videos <3 Thanks Patrick your a life saver

[lilweezycashmoney]

can anybody explain to me the setup for shell vs. disk method and when it rotates about the x or y axis! like how are you suppose to know when to insert the x's or the y's for each equation? is there a rule regarding that?

[CrayzzKill]

Light Bulb! Finally figured out what JMT is in your name.

Just Math Tutoring

[DBZfallOFman]

compared to my hs teachers and my college professors you are on the level of a hs teacher.. and that is a very good compliment because my college professors teach it very "formally" and it is very hard to understand but i understood it all in hs and you make it understandable again! thank you!

[thatharleyone]

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

[rr5001]

so when you use shell method and rotate vertically, you use terms of x; however, when you rotate horizatonally you use y terms?

[rr5001]

Why is it that integration, by making a radius and height give you the volume if your only dealing with 2d figures?



[rossgload4ever]

@rr5001 ur making them 3d figures by rotating them around axis its like spinning it around and all the area it goes through is what ur trying to find

[xxcowslayerxxx]

can you integrate sin(x^2) by itself without doing something wierd like fresnel C integral?

[patrickJMT]

@xxcowslayerxxx no

[Mrjammintime1]

@xxcowslayerxxx  Use the half angle identity

[staronline1212]

@xxcowslayerxxx 1/2X - sin2x/4 + C i think... just mentally

[DominoChild]

I never knew that a pi squared even existed until now.

[kchunielal]

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

[Egomantis49]

I love you

[ACBoredz]

Love your videos good job!

[ScizorLizard]

Godly tutoring

[WowhesNeat]

You broke it down nicely, thanks!

[Mr98supra]

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

[Titaniumgoblin]

Awesome video,

[RashaTwain]

The background noise is annoying me. What is that a chainsaw?

[newsubject89]

@hotshot226......yes cylindrical shell method can be used for any problem however some problems it is easier to use disk and washer method, you just have to distinguish which problem it would be easier for.

[HOTSHOT226]

Does anyone know if the cylindrical shell method can be used for any problem, and replace the disk and washer method?

[assbelonker279]

i wish i would've found these videos earlier. u've been getting me thru calc so thnx a lot for that. my teacher sux compared to u. n i've been paying a decent amount of college tuition for an education that i could've gotten on utube.. america's skool system sux :/ but thnx for the videos, ur my savior :-P

[sano0311]

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.

[josephtanaya]

wow its way easier when you explain it. thanks!

[sarakitdotcom]

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.

[spencerpare]

CALCULUS DOPENESS

[aksmy3]

wow! u r close to a thousand videos!!

[ratumblr]

you're a genius. will you marry me? please?

[jerstangg]

are there certain problems where you should specifically use washer/disk or shell methos?

[joejacksonriley]

You should do some physics or chemistry lectures (AP)

[andyplace]

Best teacher I've ever had!!!

[armhurt]

wow relief...

[softballchic]

I love your handwriting. I want it.

[KardOfHeart]

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

[bhujwalaali]

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

[cridge041094]

i know that it would kind of annoying for you to do the integrating and actually finding the answer, but if you could put some of the answers for your examples in the description that would be great for me when i check my work. THANK YOU SO MUCH!

[kaysterG]

@cridge041094 Just plug them into wolframalpha, it will tell you the answer so you can check.

[NateTheGreat555]

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

[GeekJonesey]

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

[mzadreexs]

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

[Seraphimaltair]

when you are making the square for the shell height, does it matter where you place it in between the two functions? or should you always place it where the hieght will be the largest?

[becsishere]

I recommended your videos to my friend before a test, and we agree that we learn more from you in a 20 minutes video than we did in 3 class periods in our class!

[aznboigotzfire]

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

[xCod3Blu3x]

learned in 20 minutes what i couldnt learn in two hours today. thanks

[newpurgatory]

don't we want the area of a circle instead of the circumference? Or am i thinking too much like the washer method

[notavailable51]

How come the shell radius is (x+4) when it is rotated about the line x=4 but its (10-x) when it is rotated about the line x=10? I don't understand shell radius!

[netshater]

@flsm11 I'm in calc 2 and im learning this stuff

[flsm11]

What year of calculus do you learn this?

[megelizsnyder]

I LOVE YOU SIR.

[adrian0120]

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!

[hiBrianhello]

who is the dude mowing his lawn

[oneunderall]

holyshit it makes sense

[danieljb300]

Do u use 2 pi in with this because its rotated around the y axis? Or is there some other specific reason? Cuz with washers u just had pi..so..whats the difference?

[Kasuaxet]

nice excellent!

[Madafucca]

When would we use shells over washers?

[thebuzdar]

@Madafucca use whatevers easier

[xstevemeatx]

can you please do one on hydrostatic pressure/force? section 9.3 in stewart calc book

[aboazam1990]

I really dont know how to thank you i was stuck in the homework and now everything cleeeeeeeeeeeeeeear thank you very much : )

[BrookeWashburn]

Pretty sure I love you. Move here and be my tutor. Pleeeease.

[BrookeWashburn]

I love you. Move here and be my math tutor. Pleeeease.

[belyrodr]

Hi I have a problem similar to this but i have no idea how to solve it! :(

it says: Consider the given curves to do find the volume using cylindrical shells by rotating about the x-axis:

64y=x^3 y=8 x=0

usually watching your videos would help me understand my hw but I cant come up with how to solve it this time! Can you help me please?? :)

[gulloogtg]

KISSSSSES from LA



[bloodsssssssss]

is there any good site which have Physics tutorials. Im taking university physics after 4 years and i;m having problems. Would be great if there is a site for physics. Let me know anyone.

[gulloogtg]

@bloodsssssssss

youtube,, PHYSICS 8.01

8.02

8.03

YOUTUBE IT

[PhxPride1]

Where do the "2pi" and the "x" before the rest of the integrand come from?

[patrickJMT]

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

[HOTSHOT226]

@patrickJMT Patrick, little help man. Are you saying that the cylindrical shells method can be used for any problem? And I never have to do another disk or washer method again?

[commhealy]

@PhxPride1 it's an application of related rates using a familiar equation from the perimeter of a circle. You can take entire classes in calc on just related rates though the equations you use are usually more involved than the perimeter of a circle.

[kritiRm]

you make calculus borderline fun :)

[patrickJMT]

@kritiRm i will take that as a compliment ; )

[richards123456789]

you are a lifesaver! thanks so much for these videos...trials for maths tomrorow :S

[TheCoolfez]

Hi Patrick, I am confused on how do you know when to use disc/washer or cylindrical shell method? You can message me at gxchen89@gmail.com

Thanks so much!

[GuildmistressDeby]

how do you know when to use this method? can we use it in any case?

[football5770]

Why don't more professors, use this style of teaching.

You cover the same material, but it flows logically and in a path rather than the jumbled mess my previous professors seem to go by.

You sir are a god among men.

[TheCoolfez]

how is the shell radius =x? Is that always the case?

[Cruth8987]

how is this one 19:55 in length, u love us long time

[patrickJMT]

aww baby. you know i do.

[kalasko14]

it was the best video that i've ever seen, thanks patrick, you made possible that i can understand that method!

[patrickJMT]

@kalasko14 glad it made sense : )

[victoraca]

there is someone mixing something in the backgorund

[patrickJMT]

@victoraca mix master mike is cuttin it up

[4thKyuubi]

What would your radius be if your limits of integration starts from a negative number instead? Is the radius still going to be x+(distance of graph from y-axis)? Say, from -1 to 2. What is the radius exactly, is it the distance of the function from the line you are rotating about?

[kittykitty42]

@4thKyuubi right point minus left point or 2- (-1) or 3

[dh4031]

Yes the asians love you very much!!! ^.^!!

[Karayzian3]

this comment is long over due but thanks for all the vids!! keep em' comin'

[NoraPeters]

You save my life every time dude. I love you

[joshuaoladiti]

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.

[tanim80]

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

[AmberinTrees]

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

[patrickJMT]

@AmberinTrees glad it helps!!

[thickwestcoastmami]

you are absolutely amazing!! you really just saved me from my calc test tomorrow. THANK YOU THANK YOU THANK YOU for posting these videos =]

[thickwestcoastmami]

you are absolutely amazing!! you really just saved me from my calc test tomorrow. THANK YOU THANK YOU THANK YOU for posting these videos =]

[Prolocater]

great job man this video was more help to me than my teachers explanation

this will help me on my final tomorrow

[4thKyuubi]

One question, when using cylindrical shells vs disks/washer methods, do i get the same answer either way?

[4thKyuubi]

@4thKyuubi oh never mind

[MovieDirectorUncut]

wish my teacher could actually teach... like this...

[wwoolsey09]

hey is there any way you can post a video showing us how to find the volume of a taurus using the shell method? btw love your videos everything makes perfect sense!

[fuddckbush]

Big test tomorrow thanks for all the help. I studied the entire section from your videos. I sat on my own trying to figure it out for hours and started hitting my head. BLAH. Thanks for everything I really appreciate it!

[tete9000]

thank you very much:}

[mrgreek21]

i fucking love you.

[thieving1]

i FUCKING love you too!

i have a final for calculus tomorrow here @ UCLA and this was sooooo useful!

<3 thanks homie!

[kpr1968]

Because the phrase " rotate around the y=?" actually means that you're integrating (from zero to 2pi) the function x, d-theta. evaluate (x*theta) from 0 to 2pi gives 2pi*x minus zero. That x shows up as the "shell radius." How did I do?

[gemstonemillenium]

Thanks, tomorrow I have class for calculus, and a quiz. After I watched the video, I am not confused anymore.

[Becaamazing]

Why is it 2 pi??

[polishboxer22]

Remember we're doing volume of a cylinder, and the formula for that is 2pi(radius)(height). Another way to think about it is the area of the circle multiplied by the height, hence the 2pi. Hope that helps.

[jackrabbit123456]

its just the general formula

[BlueElectric13]

why do i bother going to school? haha thanks  for this vid!

[vortex85242]

can you do it revolving around a horizontal axis of revolution?

[lorafay3]

@vortex85242 it's at 14:07

[ragusajr]

Long live the Math geeks!

[coolcarly25]

best videos ever!!! :D

[Moogles7878]

You definitely have a gift for explaining things! You just saved me from failing my upcoming test, thank you!

[yuzdeelli]

i love you

[chico51392]

Thank you so much! Awesome explanation.

[mrbluenight89]

Wao! man u r owesome.

[amrichbiatch]

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

[anji0san]

Thank you millions times

[kthrasher413]

dude your the man. Calc made easy

[metalfreak1892]

explanations dont get any better than this!

[phatl12345]

haha me too. I had fallen for your voice. Everytime I hear it my brain feels very hungry for your knowledge ! love to learn from your videos. Truly appreciate it <3

[aksmy3]

@phatl12345 I wanted to play a video the other day and I was like " let me got to the other room ,this might disturb u guys", and my family was like "oh! its ok we love his voice."

lol

[Mnangagwa]

Awesome !

[NicoThR]

Love you..

[RobBrown822]

Ghetto fab!!

^^imo =p

[teamoferforever]

this totally made sense! i'm not trying to be hard on my prof but I just wish she could explain EVERYTHING as clearly as you do. Thanks so much!

[Chavostyle31]

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

[picsparks]

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

[alexPsanz]

heym u hear this all the time but, u are a baller dude, for real. these videos replace my teacher.

[dmsfid7205]

never had this clear explanation ever!

I've fallen in love with your voice

[Alain0775]

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

[andreablacker]

thank you thank you thank you.... if i get a good grade in my final ... you'll sure to be the reason why!!! Thanks for doing this videos =D...

[greatmoose]

<3 :D HELPED SO MUCH

[kovid87]

thx alot

[scorpio327x]

I dont get why do You make the x isolated when your solving the problem? ( 14:04)

[kaitamasaki]

Cylinder shells by default are solved in terms of X

blah blah blah DX, with the rotation about a line X = something

here its in terms of Y = something, and since the integral will be blah blah DY, then we need x = Y instead (inversed)

[syriankid4ever]

Thanks a lot now I understand much better.