Volume of rotation: cylindrical shells about the x-axis or y= (KristaKingMath)

► My Applications of Integrals course: www.kristaking...
Learn how to use the cylindrical shells method to find the volume obtained by rotating the region bounded by given curves around a given axis. In this particular problem, we'll rotate about the line defined as y=a.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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[@salmaalyahya8916]

Your majesty, Krista King, your videos are helping millions of people. What a queen

[@andregirardifarhat]

I'm from Brazil and I'm learning it at the college. Congratulations, your video is completely clear and your voice is so sweet! Very useful!

[@kristakingmath]

Glad you liked it!

[@robsonnonato3517]

I too.

[@charlesrivers1866]

Ms. King, I'm a navy guy who started knocking out classes a year ago when he got on shore duty and am just a couple classes away from their BS degree... and just started taking Calculus 2 after having passed 1 several years ago underway with little more than a TI-89 and a textbook. The online course I'm taking now isn't much better, with everything being pretty much self-taught. After hours over the last week, after the course started, reading the text book and watching random videos... I happened upon yours and got my first few lightbulbs. It's very appreciated. I couldn't even work the study problems that had the answers but you explaining your way through an example problem was what I needed. Best wishes to you.

[@kristakingmath]

Thank you so much, I'm so glad the videos helped! Thank you for your service, and I hope the videos can help through the rest of Calc 2! :D

[@charlesrivers1866]

Ms. King... I just wanted to follow-up with you. I managed to get scores in the 80s on both my midterm and final and turn in some decent course work. Final grade was a 91 overall in the course! I'm starting the next-to-the-last course this coming Monday for my degree and this and the last one are no-big-deal after that Calc 2 hurdle. I've probably watched half or more of your videos related to Calculus 2 over the last 3 months and you gave me more 'lightbulb' moments than any other resource I used. Thank you so much. While I didn't end up using it, I did see you have a tutoring service and I hope it is a profitable venture. I've recommend you to several people and will continue to do so in the future. All the best to you and yours. V/R Charles

[@Yaowza1227]

You deserve a medal for your hard work! You're so consistent with videos and topics, and it's a ton of help to college students like myself. Thank you so very much!

[@katnoah7903]

Been looking for an easy way to organize ideas and the chart you made helped A TON. Thanks for saving me some time searching for answers!

[@Andy-jw4tf]

Glad to see this broken down and explained very thoroughly, thank you so much!

[@eloofant]

thank you so much im struggling in my calc 2 class and i really want to thank you for your videos!!

[@kristakingmath]

Glad you like them! I'll definitely continue with the videos. :D

[@TechVenturer]

you are great. everything i learnt in class only confuses me. but ur tutorials are really helpful. great work !

[@RSPSify]

Just saved me a few hours, I'll be watching your videos on the rest of calculus if you have them, love the notes

[@kristakingmath]

don't feel stupid, because you're not! these are just hard, and i should have made a clearer video! for your problem, you have a solid cylinder laying on it's side, right? you need to use disk method, because you only use washer or cylindrical shells when you have a hole in the middle, and yours is solid. watch the first video on this page and scroll down and look at the table at the bottom, it should help! integralcalc(dot)com/volume-by-disks-and-washers-about-the-x-axis-or-y/

[@widuraelkaduwa3192]

1. It might mention in the question 2. Try to draw a washer, if u can't, it means it goes with cylindrical shell method

[@hg2.]

"Getting there" on these cylinder problems. Good illustrations fir visualising what's going on.

[@EricNunezthehomeloanguru]

Seriously, you make things so easy. Thank you so much!!!!!!

[@PeoplezDecide]

So much better than my teacher, please continue with videos!

[@bkboggy]

Well done. Very clear explanation.

[@kristakingmath]

Receiving comments like yours makes it all worth it! :)

[@kristakingmath]

That makes me smile. :)

[@profearthurito6993]

CONGRATULATIONS SISTER TEACHER KRISTA KING!! THANKS SO MUCH FOR SHARING YOUR MATH KNOWLEDGE. BLESSINGS AND GREETINGS FROM SAN JUAN DE LURIGANCHO, LIMA, PERÚ!!

[@kristakingmath]

Thank you so much, Arturo, I really appreciate the support!

[@profearthurito6993]

"DADDY GOD BLESS YOU, SISTER TEACHER KRISTA KING"!!

[@joscelynmarquez8127]

I think I love you. Thank you so much! You explained it way better than my professor did.

[@kristakingmath]

+Joscelyn Marquez You're welcome, I'm so glad it helped! :D

[@blotchyt]

Thank you so much!

[@kristakingmath]

I've got some calc III done already, and looking to make more. :)

[@solariaeuropa3669]

I have been struggling with these alot, Thank you Krista!

[@kristakingmath]

I'm glad it could help!

[@Abbas-us7zu]

Thanks for solving this problem

[@kristakingmath]

You're welcome!

[@kristakingmath]

no, usually there's a correct method to choose, and you'll only end up with the right answer if you pick the right method.

[@rgcalderon3458]

I'm confusing the shell method and the washer method. Wouldn't any hole in a disk be a cylinder or a washer in some way? This is giving me trouble.... I don't know which one to use when there a whole in the middle...

[@georgieporgie6920]

thank you so much! integrating by disk is so much easier!

[@kristakingmath]

you're welcome! :D

[@kristakingmath]

Thanks! I'm glad they are helping! :)

[@sugarflowers1]

This is exactly what I was looking for thank you!

[@kristakingmath]

Yay! :D

[@Voi35con]

i love the video, omg. I wish I watched it the beginning of the semester

[@kristakingmath]

i'm so glad you liked it! :D

[@kristakingmath]

I'm so glad! You're welcome! :D

[@germandrummer13]

i don't understand... can i do this by the disk method? I'm setting it up, pi*(definite integral bounded 0 to 1) (1-x^3)^2 dx what am i doing wrong?

[@nejatahmed1584]

O God! long life! your videos are helping me so much! they are helpful! Thank you so much!!!!!!!

[@kristakingmath]

+Nejat Ahmed You're welcome, I'm happy to help!

[@pietrom2]

I struggle with determining the radius, both inner and outer. Is the outer the function measured from the y or x axis? Conversely, is the inner radius measured from the same axis to the shorter function, ie y=x? What is the general rule though for determining radius in these volume problems?

[@hoswayh7163]

thank you for making this easy to understand. Love your knowledge behind this material -quaz

[@MMikael1994]

Thank you! You reallly make it easy!

[@Jaime714Lopez]

Thank you very much!!! I have finals tomorrow and you just cleared this up for me. Thank you!!!!!!!!

[@kristakingmath]

So glad I could help you prepare! I hope your finals went well! :D

[@TastyButter69]

Will using the disk washer method or cylindrical shell give you the same answer?

[@alfredocumbana5923]

very well explained, thanks

[@kristakingmath]

+Alfredo Cumbana You're welcome!

[@rafaelmolina5641]

Very helpful! could you show this problem though, Rotated about y=-1; x=5(cubed root)y ; x=5y^2

[@almatnarmatov]

Such a sweeat voice! I love it!

[@Jezebel1115]

Hell yeah, I found this video helpful!!! Thank you so much for sharing!!!

[@kristakingmath]

And thank you for commenting! :D

[@danielgultom5859]

You just saved my life. Ty

[@kristakingmath]

+Daniel Gultom You're welcome, I'm glad I could help!

[@peteraguer1569]

Thank you..your videos helps a lot..Now I can smile as I wait to take down midterm,,

[@kristakingmath]

You're welcome! I'm so glad the videos have been helpful... good luck on your midterm, I hope you do great!!

[@asnsr3573]

So much helpful!!!! THANK YOU I like the notes very much

[@kristakingmath]

I'm so glad it helped!

[@jameshaws9986]

wouldn't the bouds of integration be 0 to 2? Since it's about y=1 the rotated function would cross the y axis at 2.

[@joelmaim8925]

That was very helpful!

[@cubfan23100]

Great videos. So helpful! thanks!

[@LHLiu-jk8sl]

isn't the volume formula pi*r^2 h? why do we use the formula for the surface area of the shell*h? Thanks!

[@anthonymachac5898]

Do you mind telling me how did you get X-1 again, because I do not understand?

[@RogerKlauser]

Hi so I was a bit confused on when to use the shell method or the washer/disk method. Can I use either method or does it matter when to use one?

[@worldxgame]

wow thank you I was searching for this.

[@progressinthemaking6732]

Hello Ms. King! How would I go about, locating the charts from this video and the disk and washer video? Do you have a link to these charts? Thank you for your time and the awesome videos!

[@kristakingmath]

Love when that happens! :)

[@100equus]

Excellent explanation of a very confusing procedure.

[@kristakingmath]

Thank you very much!

[@tiffanytse292]

When do I use the cylindrical method vs the other methods?

[@universe_expansion]

Thank you!

[@kristakingmath]

you're welcome!

[@studiant3004]

You're amazing thanks 💚💚💚💚

[@kristakingmath]

I'm happy to help! :)

[@xdrap1]

what is the app you use ?

[@Soumisoumsoum]

okayyyyy you're amazing ! :)

[@kiaraeochoa]

How do you know which method to use?

[@MsReeses97]

when you are finding the radius for this problem I get why you have the one but why did you have to subtract the y from 1?

[@devinbeverage5199]

We subtract the y from 1 because y represents the distance between the x-axis and the outer part of the cylinder, and 1 is the entire length between the x-axis and the axis of rotation. All that's left is the distance between the outer part of the cylinder and the center of the cylinder.

[@baburo101]

Thnx

[@143sylar431]

Why is the value y in 2pi the radius when the function itself makes up the radius for the rotated region....? this doesn't make any logical sense.

[@steve21889]

Thank you!!!

[@kristakingmath]

steve21889 You're welcome!

[@falalakim]

thank you so so much

[@kristakingmath]

you're welcome!! :)

[@rajslietster]

nicely explained Thanks!

[@kristakingmath]

Thanks!

[@J1ffyLub3]

this helped a ton. thanks :D

[@kristakingmath]

you're welcome! i'm so glad it helped!

[@pinkybananas1]

what has to be set equal to each other in order to get the limits of integration?

[@kristakingmath]

+pinkybananas1 The two curves that are defining the inner and outer radius.

[@javiermonarrez8666]

Hi Krista, could the same method be used for y=square root(x); y=2; x=0 revolving around the x-axis?

[@kristakingmath]

Absolutely! :)

[@coolfern37520]

Would the radius be y+1 if it were rotating around y=-1? Thanks for the video!

[@jaypatel-bp6mj]

Yes

[@ahmedalkhalifah6973]

hello my problem is how to find the radius

[@JoseGuillen422]

Seriously this method has me so lost, well trying to find the radius 😅🔫

[@kristakingmath]

This is one of the toughest calc topics out of all of them! They just take a lot of practice... don't give up. :)

[@danieljakimiu]

Tongue at 11:12

[@ashleighmcadams2729]

What if you have two functions? (Creating a washer instead of a disk).

[@kristakingmath]

Then you follow a similar process, but you use washer method instead of disk method. Here are a couple examples: kzbin.infosearch?query=washer

[@axcelotl]

ur a god

[@givemexoxoxkthanx]

heyyy girlie. you know i love your videos, i depend my life on them, but you lost me. big time. after 7-ish minutes. first of all, i'm not even sure i'm using the right method, but i'm working on a y=9/x, x=1, x=5, y=0 about x axis, and i couldn't track my cylinder...idk if i need it. i feel so stupid. help?!

[@FulAlseyab86]

do you have a differential equation course on Udemy ?

[@kristakingmath]

I don't, but I have quite a few different DE lessons at the end of my Calc 3 course on Udemy. If you go to the Calc 3 course and scroll down through the curriculum, you'll see them there at the end. :)

[@LuckieDuckkTTV]

I can't believe she multiplied to 2pie before that piece was added up lol makes it so much harder to do it that way

[@Soumisoumsoum]

DO CALC III

[@impermissa]

Where can I find a girl like this? There's definitely none in my calc class. I must not be going to the right school. Fuck

[@kristakingmath]

I made a page here detailing everything :) integralcalc (dot) com/how-I-create-my-videos/

[@MrMoeqt]

your soooooo amazing and pretty:P

[@Ryan-ue9ve]

I wish I had your brain. I tend to over complicate things!

[@kristakingmath]

I understand, I do that too sometimes!

[@deancoffman250]

hot

[@buketozklnc8937]

your video is very useful but the method is not :D

[@Getaneh188]

robot