Longer Version - Volumes using Disks/Washers

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Longer Version - Volumes using Disks/Washers - In this video I do numerous examples of calculating volumes or regions using the disk/washer method.
For more free math videos, visit PatrickJMT.com

[@georgehanna8768]

The noise in the background is coming from the monster that is responsible for bad grades.

[@tamannaalam2938]

still waaaayyyy better than my prof.

[@kicksomeup6998]

+George Hanna They are called satanic electro-farts.

[@azizm0]

HAHAHAHAH MAN

[@ACTlVISION]

Some say it gets louder when you're watching this the same day as your calc final

[@diy-projects]

@@ACTlVISION I can confirm

[@FarrisTX]

You are the best person who can teach math on KZbin PERIOD. Every time I take a class in math or I have to teach someone math I come right to your KZbin Chanel. Keep the great work.

[@jeshudastidar]

I usually don't comment on your stuff but truly appreciate it. However, as I'm eating my cereal 6 in the morning and watching this, it clicked in my head. I just have these four words to say, YOU ARE THE BEST! I wish you see this. P.S. I'm trying to learn cal 2 on my own.

[@grantmarshall6843]

i know im a little late but good luck lol. How'd it go?

[@diags_1109]

@@grantmarshall6843 Ya howd go Mr.WOng ohh well I go my phd now

[@RisesInTheYeast]

patrickJMT changed my life

[@WretchedRecordsUS]

that should be on a shirt

[@chadliampearcy]

PatrickJMT is pulling me up, from the cliff I'm hanging onto with my shirt.

[@brooksolney3250]

The important points you made outweighed the horror of that screeching noise. I've been having trouble with units 7.2 and 7.3, now onto your video on the shell method!

[@nadiavasilenko4082]

This channel is by far the best I've found for math tutorials. My calc professor is useless and these videos are currently saving my life. Seriously, i love this dude

[@patrickjmt]

@cyborgninja74 yes, you can just find the points of intersection and take a number in-between those, plug it in, see which is larger and which is smaller

[@michealtekler6316]

This guy is amazing! I sit in lecture watching my teacher constantly messing up examples and going off on tangents.. But this guy has made Calculus way more clear!

[@malgorzataigras5212]

you are the best Pat - clear, to the point, convincing etc. - all the best from Ireland

[@shafinsarwar6448]

its 2019 and i am watching this...11 years ago you uploaded this video,when i was in class 6,now i am in 4th year of my University level...Thank you sir,your teaching skill is awesome...

[@patrickjmt]

i have quite a few graphing... a vid on basic graphs you should know, along with graph transformations... perhaps those will help! if not, let me know more of what you would like to see.

[@danceinlove98]

OH MY GOD WHOEVER YOU ARE PatrickJMT THANK YOU! Seriously, my teacher is the worst but his exams are hard. You saved me. Infinite thank yous

[@patrickjmt]

no, it really just depends on the functions given : ) although if you look at examples from a lot of textbooks, i could see how you would get that impression : )

[@jarjarannoya2]

Thanks to you, I was able to skip precalculus completely and go into a very compressed, sped up, and challenging calculus 1 course in a summer semester and come out of it with an A....and I'm in high school!

[@CBeard98]

I don't know how my professor made finding the radius so difficult. You are a great teacher. Thank you

[@mudkip6311]

Hi Mr. Patrick, Thank you for your kindness and allowing us to learn from your videos for free. It's useful for many people and I'm very grateful for them. Thank you so much!!

[@patrickjmt]

you are most welcome :)

[@patrickmoloney672]

Patrick is so good and fast at explaining maths that he should charge per minute. It takes him 20 min to explain application of integration (volume).

[@gargleburry]

why aren't these people our teachers

[@SukhdipKaur]

That was deep, man. Well said.

[@Jeremy_Fisher]

They are.

[@RiHezBestSmiteMontages]

@@Jeremy_Fisher deep^2

[@kayisire9883]

12 years ago and it’s very clear and understandable thank you Patrick

[@patrickjmt]

thanks for choosing me first :) glad you like my stuff!

[@patrickjmt]

@Canada9318 ok, just making sure : ) it is amazing how many people skip that step so often.

[@patrickjmt]

all except the one's in my classes... : ) i am glad you find them so useful and of good quality : )

[@1khoury]

You are great Patrick. Saved my life on almost every ap calc test i've had this year.

[@patrickjmt]

@Canada9318 dont forget the most important part: work on problems!

[@nodnal1357]

you literally taught me this chapter in an hour, when my calc teacher couldn't do it in a week. you. are. EPIC!!

[@1light4love]

oh Thank God... this gives me hope. First Calc2 exam is on my Birthday Tuesday... right after my first paper is due and first BioChem exam Monday.... HAPPY. BIRTHDAY. ME. *cue Patrick🙌🎉🎂🙏*

[@MusicDJz1]

This is a hell of a lot less complicated than the way my calc teacher explained it! I love you soooo much!! xoxo

[@Cascada194]

This is by far more explanatory than the video lessons I use. Thank you.

[@ferjongew]

Patrick! I do the same! but my list goes: 1) Take useless notes from the class 2) Struggle at home deciphering a 1991 math book my professor wants me to use 3) Realize nothing works 4) Watch PatrickJMT, take notes from him 5) Finally understand the subjects!

[@Canada9318]

@patrickJMT Yes, I pause your videos and solve the problem then watch how you do it. Then of course, I do the suggested exercises. Calculus is getting pretty interesting too so that helps.

[@ashwins8173]

Thanks so much i found your disk,washer,and shell method explanations with examples very helpful. You explained it better than my teacher !!! :)

[@BrownieX001]

This somehow made more sense than anything I have done before. I don't know why maybe it was the whistle but you explain like my professor but I understand you more than him. I did not get these integral application problems until I watched a couple of these videos in the integral playlist. Long time follower and still being confused and then helped by you. Thanks.

[@patrickjmt]

@SolitaryAngel917 yep

[@omardahbali5596]

You are a life savor Pat so Thank you. Two professors along with a friend of mine have tried to explain this to me but I failed to understand it till now.

[@Bakugantsuvai1]

Damn... why doesn't this guy have a KZbin Partnership already! This guy is more concise than KhanAcademy in some scenarios and this video is one of them.

[@gibbousm]

i like your videos, just wish I had found them earlier in the semester rather than right before finals but they were great in helping me review.

[@TheMWKH]

I really appreciate your work on making things easier for us to understand. Keep up the good work!

[@patrickjmt]

+Meutia Hakim thanks! I'll do my best! :)

[@MrAlbashiri]

Thank you. You are the best. You explained what my tutors and university couldn't. Love you.

[@mrgames4people]

11:48 I had an epiphany and everything clicked! Patrick is truly a god among men

[@patrickjmt]

it feels so good when it all of a sudden makes sense! i've had so many of those moments

[@RogerKlauser]

Patrick, thank you so much for all of your help. Your videos have helped me out ever since the beginning of calculus. Mid-term is on Tuesday, and now I feel prepared!

[@moinaction]

How do I get my donation to you? You're a life saver for many students. Whatever we all can do to help so you can keep making all these videos for generations to watch. Thanks

[@tinaMONSTUR]

I have a final tomorrow and your videos are really helping me understand the materials. I am very grateful and thankful for them, god bless.

[@patrickjmt]

@xshanayy wonderful! : ) glad you like my stuff!

[@eggman1112]

youre a beast, I was struggling with this topic for weeks but your video got me through it in 20 minutes, THANK UUUU

[@patrickjmt]

@NovaSazoku yea, this video does unfortunately. this is what happens when you are broke (poor equipment) and have no idea how to make videos : ) (that is, this was an earlier video)

[@saladking2370]

I'm so glad you put a negative axis example, I couldn't figure it out

[@MTB-Josh]

That arrow method to find the inner and outer radius saved me! That was the only part of my next test that I was having a hard time with for some reason. I was looking for a technique and of course you come through! Appreciate it!

[@erdemgezici2132]

honestly this channel has bad and reaaaly good sides. i dont listen my prof and math lesson cuz of you but i get more than 85 from exam thank you soo much

[@mistersirisaacnewton]

i was failing calculus and doing really poorly on the tests, once i started to watch your videos, my test scores went above the class average. Your videos are so helpful!!

[@accel103]

19:17 confusing?? this was crystal clear jus like all of your videos! thank you

[@mr.ode22]

hey man it's been 10 years and you're still the goat for helping me in everything math, i hope you're doing well

[@tuliosheihee7204]

on 6:49, the answers in A, B and C are pi/6, 7(pi)/6 and 5(pi)/2 respectively

[@sravanibhukya2933]

Great..after watching many videos I got this one ...crystal clear explanation 👌

[@prcushinplaya08]

Wow. I was terribly confused by the whole (8-x) thing, with the distances and such. Incredibly helpful. Thank you.

[@WompyConk]

Does anyone else seem to have an easier time learning from Patrick than through your own teacher?

[@jumanafathima8853]

Thanks for all the work you put into your videos. You've continued to help me throughout my math in high school and college, and I can't thank you enough!

[@MundusLitterae]

Awesome thanks. I used these videos last semester for Cal I and now I'm still using them for Cal II :D Thank you so much!! You were able to explain everything so easily and clearly! :D

[@taeyang]

I wish I had known about patrickJMT before, EVERYTHING MAKES SENSE NOW ! Test in two hours...

[@MadJDMTurboBoost]

What if you want to rotate around a function like y=x+3? Would you incorporate that just like the y=8? Like [(x+3)-(x)] ^2 - [(x+3)-sqrt(x)]^2 ?

[@thriveclub]

You saved my life. If only my teacher explained it this way! Thank you!

[@patrickjmt]

my pleasure

[@UAa320]

Patrick you're the best, this makes much more sense now thank you so much for explaining this concept.

[@bAdDA5z]

i really like the arrow trick he shows to find the big radius and small radius.

[@1230lilyjune]

Patrick you are simply amazing. If i were a college professor, i would attach every link of your video to the syllabus. It will make everyone's life so much easier

[@happyboy1029]

thank you soooooooooooooo much, you're a life saver. your explanation and view on this is so helpful. my professor over complicates things and makes it harder than it seems to be.

[@BdonYoo]

Holy shit... I have a mid-term coming up, and my chances just went from hopeless, to pretty damn good!! Thank you thank you thank you!

[@sgyniguez]

Patrick I have a question. Can you please explain where pi came from in the first example? You know, when you multiply the integral by pi?

[@shalinighosh516]

You are literally the best . You can explain the difficult concepts in such a manner that even a layman can comprehend. Keep making these awesome videos. Much love from India. :)

[@rookiebluefan]

Thank you so much for making these videos! You're literally helping me survive my calc class!

[@vonjosephmapa6276]

you didnt have the most advanced studio but your penmanship and the way you explain things are much better than those who have the advanced way.. everything was clear except for the annoying high frequency sound.. hahaha.. made me second guessed if this was physics or calculus.. xD keep up the good work. :)

[@iSmileForYouxNot]

Thank you! I didn't realize what I was learning in class was actually pretty easy

[@cheesesandwich12]

I think I speak for many calc students when I say washers are one of the most confusing concepts to learn, but you make it seem so easy and I wonder why I ever had any trouble at all! Thank you so much :)

[@jevcampbell2301]

God bless this man's soul. Even in 2020 through corona crisis, his videos are the light. I swear the amount of help he's given me. Gives me hope to remain at this university. Man, your videos will help Thousands. If I graduate I will be putting you in my speech.

[@patrickjmt]

ha, happy to help :)

[@patrickjmt]

@JoshBuntu ha, that sounds like a lot of responsibility

[@lamiah3197]

Thank you so much! That was really helpful for my final exam, you're way better in simplifying it than my professor

[@yashkapoor5894]

This was brilliantly explained. Thank you buddy! Understood this topic in 20 mins! :D

[@nexsus96]

You are a true hero with your channel.

[@mikecough3749]

I love this guy!! Even though he doesn't have all the high tech display like Khan he is way better! I Love the sharpie and paper...old school.

[@bluemagoo9219]

You deserve the most advanced studio!

[@jbear395]

6:20 "... kind of look like the tip of a bullet, to use a violent example..." lol

[@rolando0151643]

This video is 100x better explained than the actual book; I don't know why the book makes it more complicated when explaining this.

[@xxk4ixx]

I always had trouble with the revolution over anything that's not the x-axis, or the y-axis. I do have one question though, is it more appropiate to use washer when revolving vertically, and shell when revolving horizontally?

[@JUNGGEYY]

Thanks!

[@xtrickyaznx]

hey patrick do you have any videos where you're doing the function in terms of y? I am still a bit confused when it comes to a y function

[@zain4019]

Combining forces using khan academy and pjmt is just perfect for this concept

[@Jono.]

Good ole Patrick integrating binaural audio into his videos to help us retain even more!

[@georgeabreu6392]

Skills.

[@xrocabusx]

Men this guy is the best... I am taking calc 2 and my teacher is a complete moron .... I watch patrick and knowledge and understanding appear....

[@mhskyblue123]

You are truly Sin Pi ....see what I did there? But seriously your videos really help with understanding the concept in such an easy and efficient way! Got my calc exam tomorrow so learning from your videos, wish you were my calc prof :/

[@Valhala112]

Bullets aren't violent; killing is. Other than that, great vid! Sooper clear and elucidative! This'll surely prepare me for the new semester (2 days!)

[@jamesrandall5844]

man your good at explaining these things. I have been watching your videos for Calc 2 and it makes sense to me now due to you. thank you so much

[@XXKERRAXX]

this was EXTREMELY helpful, tysm, def gonna pass my calc test tomorrow

[@westonmulenga6421]

i thought i will never understand this Topic as i was really confused in class today BUT am now ok,i get the all basic idea THANK U SİR

[@Kape1One]

Thanks! You're the best. Two quick questions, was the answer for the 1st Q 8pi? Was the second answer using the Washer method 1/6pi? Thanks!!

[@dhooy7150]

How do you know when to subtract the outer squared minus the inner squared? Sometimes you don't need to subtract the function.

[@4thKyuubi]

So when do you exactly use the outer and inner radius squared? On the bullet example, how come you didnt do that? Do you only do that if you have more than 2 functions or something?

[@DeniseFayeJanerJD23]

Say we will rotate the solid region about y=-3 but the solid is actually attached to y=-3. Do we still have to add the number of units to the outer and inner radii? Thanks!

[@misshaily88]

Kinda sounds like a teapot whistling the entire time, but I didn't really care. This video was TREMENDOUSLY helpful. I feel a lot better about taking my Calc test tomorrow!

[@laylajameel5106]

After 1 minute of watching the video, I understood the lesson 😂, Thank you

[@jamesb101100]

im so mad I just found this guy during finals week, if I saw your videos earlier I would have an A in AP Calc

[@patrickjmt]

why violent? : )

[@philster00700]

You have demonstrated this concept better than Sal Khan, thank you.