Volumes of Revolution - Cylindrical Shells

[warmwinter0994]

Oh my goodness. You are an angel! I had so much trouble with cylindrical shells. Thank you so much! I'll probably watch the rest of your videos to help me study for my AP exam. Thank you again!

[Mangaddict1123]

I believe your shell is supposed to be "perpendicular" to the line you're going about not "parallel"

[2011carp]

ALL professors teaching at universities who dont do youtube videos need to get fired so that the youtube teachers that know how to teach can get hired

[SuperSuckittrebek]

Hypothetically, would it be incorrect to use dy and put everything in terms of y? Albeit more difficult, you would still get the same answer, no? I am referencing the point you made about rotational axes at approximately 1:08 in.

[nikvenkata]

hey quick question patrick, how do you know the shell radius is x?

[patrickJMT]

@nikvenkata cause you are ' x ' units away from the y-axis

[KD35USA]

Thanks so much, huge help. Nice to see someone help so many ppl on the internet instead of posting garbage all the time

[MrKingSTS]

7 people want to fail calculus

[pdobrinov]

Why is it that most math teachers are completely and utterly ineffective at teaching basic concepts in higher-level math in person, while smart people such as PatrickJMT can use a dry-erase board to teach effectively?

[prosnow222]

i've gone through some of the comments and can't find a post of the correct answer for the additional problem at the end of the video. is the answer -5pi/6? not sure if it is correct but i think i did everything correctly.

[david868]

Thanks for helping me get through Cal 2 :)

[amandwee]

so what if you go about x=3 instead of x=-3?

[BER2ERKER]

You're videos are perfect for brushing up or learning something new. I should already know this like the back of my hand, but I honestly don't even remember half of it haha.

[Digressable]

thank you so much, this clarifies just about everything! I wish you were my calc teacher Q_Q

[LosVideosDeLouis]

Patrick! Your videos are so helpful that I would send you heaping piles of boxes of dry erase markers just so you could keep on doing what you do! You helped me through one tough semester of calculus, here's to two more! THANK YOU!

[patrickJMT]

@LosVideosDeLouis happy to help :) good luck in the rest of your classes!

[Zaland4520]

Hello, I seem to be having trouble with this kind of problem. What if there was with y = 0, x = 1/2. How would you go about solving the problem then. This is for the first question.

Thanks

[olkst178]

gosh i hope SOPA passes so i can fail math and finally become the hobo i always dreamed of becoming

[patrickJMT]

@olkst178 lol

[melisantika]

I am very happy to see the vidoe Volumes of Revolution - Cylindrical Shells. In this video I show to examples of finding volumes using the method of cylindrical shells from you, hopefully the others also are happy for You

[Onepissite]

I am very happy to see the vidoe after you give this Volumes of Revolution - Cylindrical Shells. In this video I show to examples of finding volumes using the method of cylindrical shells.

[Ondelendo]

I Love The Video It Can Increase My Knowledge Volumes of Revolution - Cylindrical Shells. In this video I show to examples of finding volumes using the method of cylindrical shells

[bebeheuy]

Steady I Really Like This Video olumes of Revolution - Cylindrical Shells. In this video I show to examples of finding volumes using the method of cylindrical shells.

[willamricard]

Nice Video That You Share , So Very Nice Thanks You Volumes of Revolution - Cylindrical Shells. In this video I show to examples of finding volumes using the method of cylindrical shells.

[imegatrone]

I Really Like The Video Volumes of Revolution - Cylindrical Shells. In this video I show to examples of finding volumes using the method of cylindrical shells From Your

[bl3ckdevil]

A huge thanks to u !!

i don't know what i have to say ! ..

BTW : i did good at today exam .. thxxx : )

keep going bro .. : )

[gaylordNL]

THANKS PATRICKJMT...IT IS VERY USEFULL..

[Haelig]

Can you do this using the disk/washer method? I tried doing it but one of the limits leads to a complex answer.

[aserhilal]

what about if the q was in the exam and he asked to do it by using any method. why can not I use this formula "pi integral from a to be [ {f(x)}^2 ] dx " ?

Thank you. You Are Really Better Than My Professor.

[StateofMind09]

Is there a specific reason to find the volume as a shell instead of using the disk/washer method? Or, better yet, are there situations where you can use one and not the other?

[thesinnerheloves]

Thank you!!!!:)

[SSerju]

you are an angel sent to save all my calculus students.

[patrickJMT]

@SSerju ha, just a normal guy trying to help out

[stephenpawn]

As always, a perfect explanation. Thanks!

[xxcowslayerxxx]

can you find the volume of a solid of revolution rotated about an axis that goes through the solid so when you rotate it some of the volume over laps itself?

[patrickJMT]

@xxcowslayerxxx i have never seen a question like this. it would be confusing as to what exactly one means if they were to do this. it would also depend heavily on the geometry of the object

[ian559fresno]

Thanks.  A trick to remembering which way you draw the shell is you draw it "parashell" to the line your going about. Thats how I remember it :D

[ferasteddy]

hey patrick, thank you so much!! but i'm curious, here you used the formula 2pi and didn't square the two values, in the volumes of revolution one you used just pi and you squared the inner and outer functions. why is that?

[2003z440]

@ferasteddy

Disk and washer method vs. cylindrical shells method

[kromo24]

In the second example, I think you have to integrate with respect to dy.... since the rotation goes around the x-axis. please correct me if i am Mistaken.

[MrDmack2112]

how the hell do you use the dry-erase board being left handed!? I can barely write three lines in ink on paper without smearing/smudging the hell out of it, much less do calculus on a dry-erase!! props to ya!

[UnNuevoChile]

when do you use shells and when do you use disks?

[djwilliamt]

@UnNuevoChile It really depends on the situation sometimes its easier to use shells sometimes its easier to use disks. If your rotating around the y axis it might be easier (depending on the equation) to use shells. I always think of shells as shotgun shells with a little bit of thickness. Nonetheless, it really depends on the equation, when i was in college sometimes changing the y formula in terms of y then using the disk method helped more than actual using the shell method.

[UnNuevoChile]

@djwilliamt hey, thanks man ^^



[m4tttc]

technically, is the shell radius (x - -3)?

And if its revolving about say x = +3, the radius would be (3-x) am i right?

[bikeous23]

You explain it so well. Thanks for all these posts!

[sano0311]

HVALA TI .... means Thank You in Bosnian

[yelenaaxo3]

you are a miracle worker

[MadeOfAwesome23]

Simply put, you rock! I feel so much more prepared for my Calc 2 midterm after watching your videos!

[peterpatalano]

Here goes nothing, taking my calc 2 final in two hours. Thanks @patrickJMT

[kcuf0000]

how do you know when to use washers and when to use shell?

[Fulken16]

@kcuf0000 Basically you use disk/washers method when rotating about the x-axis and shells when rotating about the y-axis...., but technically you can use either one, depending on the case you could also just interchange the variables....hope it helps

[CrystalKay101]

OMG!!!!! I have a Calc Exam tomorrow and I am soooo going to pass this because of you!!! Grade Saver!!!! oh and duh, Life Saver!!!!!! Thank You! :D

[heyimanh]

Thank you!

[yerikim0413]

isnt that wrong graph?? since its -x^2, isnt the graph under the x-axis???

[HighGuy512]

@yerikim0413 but you're forgetting the "+x" term. When factorised, as already mentioned, y=x(1-x). This means that the roots of this equation are 0 and 1. Using the symmetry property of quadratics, the maximum (because the coefficient of x^2 is negative) will be at x=(0+1)/2 = 1/2. When x=1/2, y=1/4. Therefore, the graph cuts the x axis at x=0 and x=1 with a maximum turning point at (1/2, 1/4). The graph shown is correct in shape. Hopefully that has eased your mind. :)

[atimor]

im gonna make a t shirt that says: "PatrickJMT taught me calculus" and wear it to my math exam

[patrickJMT]

@atimor ha

[ironmantis25]

@patrickJMT

patrick where do you get the 2π from?

[SonOfNye]

Lefty pride.

[siuyeeyee00]

I don't get it, why is the radius of the shell x?

[HighStonerCraftForce]

@siuyeeyee00 Because as it starts from 0 and extends right, no matter the length the radius will always be x. If it wasn't touching the point of rotation, however, you might have x+2 or x-3 or something. It was kind of hard for me to conceptualize too.

[TheStep03]

I'm starting to love integral calculus because of you :)))

[dhcrazy333]

I wish I found this BEFORE I took my test over volumes by integration...

[ohgoodlord]

Why is it just... "x"? that's the shell radius right? That confuses me... Of what distance from the origin to an arbitrary place on the curve does one find x? I'm especially confused if the shell is spinning from about some other number in which it goes (1-x) or something... Help!!!

[dannyboy163]

is there an example of this exact function except spinning around x-axis?

[MKL131366]

Thank you so much for your help patrick, but I have a question; ¿It doesn`t matter if the shell radius is negative. For example if the value of X is -10 you are just going to add it so it can be X+10?.

[seaweedsupper]

The volume of the region rotated about x=-3 is 3.665191429? Did I do it right?

[lifemakesmelaf]

you have made sense out of the supposed gibberish in two minutes (i got it midway through the video) what i've been trying to learn through 2 one hour sessions of caculus! thanks so much!

[SnikendeBaby]

Thank you very much! I like math more because of you :)

[bootleg42]

Excellent video. You've saved so many people patrickJMT. I hope beautiful women of your likings physically pleasure you an absolute maximum (math term there, lol). You've saved so many people.

Keep up the good work. And for the future PLEASE put up more complicated examples of various topics in calculus. That's how we learn, from seeing and doing various examples. School only repeats the mediocre examples they give from the mediocre book.

[f0rza0325]

6 people are completely oblivious to the fact that patrickJMT is a demigod.

[taekwondo16]

i was stuck and the variation part was spot on clearing my doubt. THANKS!!

[ChIkEnFiNgaZ]

I cannot express how thankful I am to you. I've been trying to figure this out for my exam tomorrow night and i finally understand it thanks to you! Thank you very much

[SERGIOCHAOTIC]

@patrickJMT If the axis of revolution was at x=1 (and say the function went from a=2 to b=3 (as your bounds)) would your shell radius be x-1?

[halflimeproductions]

I missed a class and there is a test tomorrow.

You're a life saver.

[multipurpose101]

got a test in a few days. after this, like WTH if I get any less than 100%! i came here even after watching the MIT lecture (which was a little confusing).

THANKS!

Oh and 5 people failed Calculus.

[stevens0625]

your are a very wonderful person for taking your time to help others! thanks again for all the help!!

[zainabbeans]

you are an angel sent to save all calculus students

[patrickJMT]

@zainabbeans ha!

[ricorico33]

@zainabbeans yeahh you are righttttt,

[engrgirl322]

You are the best! ♥ Thank you so much!

[NIGBEATS]

I got a test 2maro and you may have just saved my ass, YOU F@$%ING ROCK MAN!!!

[iriey3d]

much easier conceptual presentation than my crappy book. great work!

[mzmilah1]

Thank you for taking the time out to do this...your making calculus sooooo easy for me

[liltwinshedevil]

Your videos are SO SO SO helpful!! =]

[lemonadesalsa]

hey if you're using shells and you have to find the volume of a solid generated when revolved around the x-axis, your variable of integration is dy, but are your limits of inegration x values still, or do they change to y values? please get back to me

[hasben0]

Why does your voice sound different on this video????

[PSNMarksmanSniper]

i got a question in the shell formula, why does dx stand for thickness

[username14657]

If only there were more patrickJMT's in this world...

[dh4031]

Tomorrow is AP Calculus Exam and thank you so much for the brush up! ^.^

[PrivateMartyr1111]

That helped me so much - thank you!

[4thKyuubi]

So whenever you rotate about the y axis or any vvertical line, your radius is gonna be x?

[4thKyuubi]

@4thKyuubi never mind, i got it

[SirAwesomesauce]

Terrific video.

[MovieDirectorUncut]

You definitely need to be a teacher AT MY SCHOOL

[omegasereon]

left handed bro tight

[sportrok11]

you helped me pass calc I now your helping me pass Calc II thank you

[JoeyyT20]

you should become a teacher and or tutor if you are not already you explain everything so perfectly

[HomelessMelody]

I personally prefer yours to the Khan Academy. Thanks so much!

[tehretardedbunny]

Thank You!

[shadyinside]

you are amazing

[ferramentapenna]

Thank you sooo much! Your explanation was way better than any I've heard, it really makes sense now. I was struggling with a problem, tried to do it three or four times before I saw this, then solved it in one go. Brilliant!

[aeoraji]

please kindly allow me to love you with some passion.

[ezimokha]

Im a bit confused. Isnt this method supposed to be used on a cylindrical like shape? All im seeing is a half circle?

[chimochimo100]

When they say "about the line" or "about the axis" this means that the shape bound by the curves is rotating around that line or axis, so you kinda have to picture the cylinder in your head given the shape. Ultimately, the shape is spinning around that line or axis to create a cylinder which you don't have to draw.

[Persuasion86]

THANK YOU SO MUCH!

[jensonj1]

respect

[leleylovee]

i just wanted to say that my TUTOR couldn't teach me this, but YOU can. thank you so, so much. you are a lifesaver to those mathematically impaired like myself.

[patrickJMT]

i am your tutor now.

send cash or check payable to:  patrickjmt.... : )

[fateater77777]

MAKE MONAY

[multipurpose101]

@patrickJMT but aren't you getting from the ads?

[FearedBliss]

@patrickJMT LMFAO

[tylerljacobs]

You tutor may not be able to teach you it, but my PROFESSOR couldnt even teach it. I'm glad patrick is my tutor now

[chimochimo100]

pay the man!

[betinhocr]

oi como resolvo estes problemas?

Pode ajudar?

x=2y x=y² no eixo y

y= 1+x+x² y= x+10  no eixo x

[ba6yhelen]

thanks! very helpful. much appreciatedq

[stephgoodmama]

i've watched your videos throughout all of cal 2! My exam is tomorrow so I'd just like to say thank you for being the best cal teacher I ever had!! :D

[freesk8]

Only if it is revolved around the y-axis...

Right Patrick?

[patrickJMT]

you can always 'use it' regardless of the axis - often times one way will be easier to integrate though

[freesk8]

I'm a substitute teacher teaching calculus tomorrow.

You have saved me a lot of time, and improved the quality of my teaching.

THANK YOU SO MUCH!!! :)

[patrickJMT]

good luck with the class!

[SLiM716]

do u get paid 4 this?? or do u just have a lot of free time??

[patrickJMT]

i do it for love of the stupid comments i receive.

[OoPrettySarahoO]

THANK YOU SO MUCH :)

[TeeMac009]

I love you, you crazy man!

[tennisIS4pussys]

thank you so much

[jkjkjkjk3e57457]

Can you ever use the cylindrical shells method for revolutions around the x-axis, or does it only work for the y-axis? Great video!

[patrickJMT]

in general, both methods can be used for either the X or Y axis; often times though, one method will be much easier

[lilALbanianPIMP]

YOU ARE THE F*CKIN BEST!!! (excuse my lang)

but really... ur 5 min video made more sense then 3 days of sitting in class nd tryin to figure out wtf was ogin on!!!

Thnk u soo much!

[naix319]

god pat you are so awesome!!!

[patrickJMT]

glad to help!!

[ronnnieeee]

so i've been trying to do these problems for a good two hours and this is the ONLY thing that has made sense to me all day aah. you are my hero? check

[bayshrooks]

this is one concept I have never gotten in calculus even though I made a 5 on my AP exam and have nearly a 100 in calc 2. its the morning of my exam and this is really helpful!

[patrickJMT]

everybody is doing last minute cramming!!! good luck everyone!!!!!!!!!

[jbulandres]

thank u so much for doing these vids man... im gonna go write a song about u

[patrickJMT]

nice! i wanna hear it

[jbulandres]

oh u will... as soon as i get a webcam

[puchitopiover2]

I'm learning all of this in my calc class and I find it interesting to see the applications of integrals. One thing that is a bummer is that in order for these formulas to work, the revolution must be a perfect circle.

How could you calculate volumes/areas with other types of revolutions (ovular,etc)?

[junkbox25]

Simply brilliant...

Wish more teachers could convey their ideas like you can.

[theexx123]

excellent mate, somehow this helped me finish an exercise i've been stuck at for the last 2 hours. Top notch :-)

[patrickJMT]

perfect : )

[Waranle]

5 stars!!!!!!!!!!

[patrickJMT]

: )

[GhostSigma]

(= (= (= (= (=

nice

^^

[patrickJMT]

: )