Volumes of Revolution - Disk/Washers Example 1

[djelite07]

Patrick is a prophet sent from the math GODS

[Crusader09100]

I have an exam on Tuesday. I finally understand the concept of outer and inner radius. Yours is one of the best explanations for calculus I have ever seen. You should be a teacher, if you are not one already. Thank you and am God bless you.

[azmariah94]

I WISH I DISCOVERED YOUR WONDERFUL VIDEOS SOONER! I just had my volume revolution (ch 6) test last week and got an F... ): I understand it now after seeing this. *_*

[RodFed1993]

Patrick JMT is my valentine

[patrickJMT]

@RodFed1993 :)

[soccersaves361]

thnx for the help. u forgot the units^3 at the end tho

[BrucasIsBettaThanYou]

Holy shit. I might actually pass tomorrow. :) You havveeee nooooo idea how much you literally probably just saved my grade! Thank you!

[prasoonsayami]

all my blessings for you mr patrick

[patrickJMT]

@prasoonsayami ;)

[dinasorous123]

@patrickJMT is this the washer or the disk method?

[eeckoichii12]

you're so nice. :)

thank you so much sir! !

[patrickJMT]

@eeckoichii12 you are very welcome :)

[42marthacu]

wow, wow wow..THANK you explained way much better than my professor :) MAy God Bless YOU

[djsneaks2]

I LOVE YOUR VIDEOS I GET THE CONCEPT ALOT QUICKER WHEN ITS ON VIDEO!!!!

[YJ8sh]

Thank You!!!

[1966lavc]

if the function does not have inverse so we will have one choice?

[PROTOTYPE2222]

I never thought to go to youtube to get calculus. Y we need to pay for books when its all here lol ö, thanks man more tutorials the better we save money for our books haha!

[snukka]

Thank you!!

[messi13578]

TODAY is the AP exam!!!!!!

[shelbieeex3]

Have my AP test tomorrow and your videos have been my go-to cram resource. Thanks!

[ch3rryp3psi]

oh my god thank you

[MsBabyBlue0]

Your handwriting is so pretty

[rjkahlon]

Basically, you helped my get an A on my midterm. I was so lost till I watched ur videos. Wish we had teachers like you at my university. Thanks

[SaxyBrad50]

6 people must be failing calculus.

[bethjovenbabiera]

what if y=2x?

[yeehaaaaaaw]

hey cant you factor out the pie so its outside of the integral because its a constant?

[ShadowKyuubi2750]

@yeehaaaaaaw Yes you can. And usually you leave it in pi form anyways so it's often the preferred option.

[HBMAN1995]

Seriously, phenomenal explanation. I'm in AICE Math (Trig and Pre-Calc) and this made me really confident about a surprise test we have tomorrow. Thanks a lot! Subscribed.

[nepsjg]

you teach just the way my teacher teaches but you explain it very well. thank you for your help!

[onlypolar]

Dude, I cannot tell how much I love you, no homo. This has helped me so, so much in my AP Calc AB class. You, you are awesome, man.

[lienaejer017]

! Im a mechanical engineering student and now im done in integral / differential calculus with a big help of this man, .you are my best teacher. i aced in our class with the help of this..my grades are very good because of this..thank you very much and keep up the good work!..i will start studying differential equations with this videos this vacation..THANK YOU

I SURVIVED WITHOUT BUYING EXPENSIVE BOOKS BECAUSE OF THIS! GOD BLESS

03-26-11

[maysenator]

what do you do to rotate around y-axis? could you explain what im missing i kno im just thinking about it wrong

[Seedofwinter]

I know you're busy and stuff Patrick, but how do I go about solving a volume of revolution when the axis you're supposed to rotate it on is a few units above the function?

[patrickJMT]

@Seedofwinter there should be a video of this somewhere

[Seedofwinter]

@patrickJMT Yeah I found it on your website. Thanks a lot, man.

[fingerboy18]

@Seedofwinter It's always the distance from the function to the line that it's rotating about. I call the area of the solid R(x) and the hole r(x).

[ian559fresno]

@Seedofwinter those problems are the worst.

[alshubily]

great explination

appreciated

[patrickJMT]

@alshubily my pleasure

[loojiji]

Hey Patrick, awesome video, by the way. Made it crystal clear when I was struggling a bit with it. Thanks so much. But I do have a question: when the big radius is a certain number and the little radius is zero (when the function rotates around the line that is the bottom boundary of the function), do you do big R squared minus little r squared? Or is there something different there? Also, when you integrate with respect to y, you put everything in terms of y, right?

[patrickJMT]

@loojiji well, in this case the little r is just zero as you said, so there is only one term in the integral that is being squared. yes, if you integrate wrt y, you put everything in terms of y

[MythicalSun]

Patrick comes through again. Let me extend my gratitude, Sir. :-) Be blessed, my friend.

[Jpres]

i'd fail math if it werent for you, you rock man

[razr4444]

How do you know though to use the washer method instead of the disk method?

[salo69]

I swear.. u got me through calc 1 and now u're the reason Im gonna pass calc 2 and probably calc 3 and diff eq.... I owe you too much. Im gonna repay you. just wait and see

[LethaLImpuLse]

OH my fucking god... here I am about to kill myself trying to understand Stewart's Calculus on this section.. when I can just watch your videos and understand in mere minutes. Thank you SO much!

[querpa]

Thanks, this is pretty easy to follow with nice, clean visuals. Helped me get the subject.

[Titaniumgoblin]

3:52 wait dont u have to add + C after integrating?

[mwtillotson]

@Titaniumgoblin

You only add + C for indefinite integrals.

[FuadHatem]

Thanks man, All I wanted was to find the Radius from these volume of revolution problems and u made me get it in 10 seconds!

[Shizzy77]

It's kind of scary how this is the exact same question I was having trouble with in my textbook.....

[jinglespbell]

this is brain porn!! :D annnd I like it !!

[seaweedsupper]

Wow I spent 2 hours in class trying to understand the disk and washer method but after watching this 4 minute video I understand everything. PatrickJMT, you are amazing.

[mozartandi]

you're like the BEST math teacher EVERR!

u teach so well and i understand everything when you explain it.

:DDD i owe my understanding of calc (finally) to you :DDD

[LorencHoxha]

I know a lot of Math teachers on the web, but you are REALLy the best. Good Job! :)

[crazymallu]

thank you so much

[pansh90]

YOU ARE MY HERO

[xGhost301x]

You should just be on a tv screen in every english speaking calculus class

[onyxfig]

I don't mean to sound like an ass and I appreciate all of your explanations but this is just too broad and simple. For three videos you explain something that personally I understood in about a minute. I was hoping you would elaborate on using the washer methods with dy for example or combining two integrals.

[Aznboy5454]

PatrickJMT for President

[patrickJMT]

@Aznboy5454 that is about the last job on earth i would want!

[10n3r]

@patrickJMT PatrickJMT for dictator?

[patrickJMT]

@10n3r nah, i do not want to control people. just want to be left alone to live my life, just like most people.

[lamp007]

i learned in less than 5min what i wasted most of the semester confused with...i knew my professor sucked but wow...

[lamp007]

i learned in 5min what i wasted most of the semester confused with...i knew my professor sucked but wow...

[phelix1232000]

This helped so much! I was really having trouble understanding some of this, but this video really clarified things. I love the outer radius and inner radius way of thinking.

[Econ1260MetZRoberto]

patrick JMT, you are an absolute wonder sent to us by God. I can't, for the life of me, recount the many instances your videos have helped me, buddy. I send you my warmest and deepest regards,

Sincerely Rob

[quiquemoranmoyano]

Thanks again, these videos are life savers, now I know not to panic if I don't understand something in class, sometimes it seems like professors in class are only interested in finishing the material than making sure we learn, so they rush throuhg the subject. I spend my time in class copying examples and not much time paying attention, so when I come home I go to Youtube University and for Calc, I use profesor Patrick JMT.

[patrickJMT]

@quiquemoranmoyano well, when i taught, they were like: you MUST cover this much material each day; i felt rushed teaching it. plus, tons of people get into calculus who totally should not be there. so, i do not think it is always that the profs do not care (although some certainly do not!). anywho, i am always on youtube, come back any time!

[FearedBliss]

@patrickJMT I love your work, I'm currently in Calculus 2 in college and I love math. Normally I didn't have any problems when the professor started teaching the disk and washer method. But after he introduced the shell method, I became confused. Specifically related to when should I use which method. Vox, and Voy, y is a function of x, or vice-versa, each one has a different method. I'm going to keep watching your revolution videos. Thanks for your work. Btw, I've been subscribed for a while :D

[santoyrayado]

thanks alot patrick, i got a B in my cal2 class this summer thanks to your videos, I would done better if had known about 'em earlier.... thanks

[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]

Hi, why did you square the problems? Thanks

[brndoil]

i dont get it i thought it was a video about revolution strategys or something like that

i maybe dont get the math problem cause i am only 14

[patrickJMT]

@brndoil what is a revolution strategy? like when you overthrow the government?

[brndoil]

@patrickJMT yes haha its something for my clas i wouldent make plans like that my self :D

[bloodanddirt]

x squeeeeered. 

[rohannesburg]

man i appreciate soo much of this, the reason is because, this is not a typical 2unit question, though it requires the same procedure,

But im lookin forward on a video for the 4unit Volume Slicing method cos it gets a bit complicated with more wierd shapes. For example when you rotate a region, you obtain a circular hole in the middle, ie. Rotating a parabola around the x-axis

[Pointyfoxears]

oh my god, I love you. You just saved my ass for my calc final tomorrow.

[XMethoDTK]

The inner n outer radius was quite obvious but i don't find it smiler to the other washers problems we did before.

thx anyway

[XMethoDTK]

The inner n outer radius was quite obvious but i don't find it smiler to the other washers problems we did before.

thx anyway

[livchristinemusic]

you just saved my life. :]

[machiggins]

you are amazing

[4thKyuubi]

So everytime we solve dis and washer problems we always take the integral of (pi r(sub1)^2)-(pi r(sub2)^2) to get the volume?

[AnanaMango]

@4thKyuubi If it's not a washer problem (ie. if it doesn't have a hole in the middle of the solid formed), then you don't need to do the minus the other part, because then you are only dealing with one fully solid form so you just go Int(pi*r(x)^2). That's disk method. Washer method is when you have two different functions making the shape so that there's a hole in the middle, and just like you and the video said: you do Outtie minus Innie.

[patrickJMT]

@AnanaMango listen to anana... she knows whats up!

[kingofsoulsfrombm]

@patrickJMT Yea, anna's right, but I think that the way you did it is great.

[iTzJimBoi]

I enjoyed the video and found it educational. I'm proficient with revolutions when it is based on washers and disks...it's just that when they through theoretical shapes that have no value that I start getting mixed up. Like "A base of S is a circular disk with radius r. Parallel cross-sections perpendicular to the base are squares." Can you make a video outlining the steps to approach these theoretical problems?

[TolaMagician]

OMG you make sense!!!!! nI love your videos all the others i watched only confused me more but now I get it. Thanks man

[lusixoxo]

You are the math God!

[Sector9pablopedro]

if i'm going to continue growing in my Math Classes you're going to have to make some more videos =)

[j66s66]

Thank you very much, i have no words to describe how much i admire you

[FirstClassySecrets]

CLEARLY they are neither discs NOR washers. they are donuts. come on people. =P

[Slayermagic]

do you take mat135 at university of toronto? o.O

[FirstClassySecrets]

unfortunately no

sorry

=(

[Slayermagic]

ah we had the doughnut dilemma haha

[FirstClassySecrets]

yeah i heard it from my calc prof and was horrified to take the next calc class and hear them called "discs." donuts are MUCH more inspiring.

[coolcarly25]

yes, and these helped so much :D

[hybridindian]

Bagels, actually.

[FirstClassySecrets]

I'm going to have to argue that although bagels are quite delightful, I would prefer a good donut.

[cookieplz]

you should see the torus problems. those are REALLY donuts :(

[FirstClassySecrets]

Your frowny makes me doubt that those "real" donuts you speak of are actually delicious....

[spongey17]

you just saved my life.

[gorilla199]

They are washers - Not Discs!

[desiballer123]

this is AMAZING thank you so much I appreciate it, really.

[iluassyla]

Your soooooo good man really clear n u actually teach better than almost every math teacher I ever had good job man....thnx alot.

[ecaep86]

OMG i had this problem in my calc book... could not solve it...i have a test in the morning and this washer method was annoying me.. now i get it...thank you...how can i support your efforts? let me know i will try!

[temmybear33]

@ecaep86 if you couldnt figure this simple problem on your own how did u pass your test my teacher gives us a problem thats ten times harder than this

[patrickJMT]

@temmybear33 i know it is the internet, but honestly, there is no reason to be a douche bag

[RobertSmith3]

nice job, i might just do well on my exam tomorrow :)

[Kakashinoor]

"certainly you've done something wrong" hahahahaha great video 5 stars

[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

[lysolluvswindex]

aw man! i wish i had thought of looking for something like this sooner!!! AP test is on Thursday!!! Oh well....

[mini1028]

Please teach at my school!

[treflipper]

also an easier way to clean it up is to take pi out of both and bring it outside the integral so its outer radius squared minus inner radius squared dx. etc.

[SLiM716]

dude..i gotta reteach this stuff to my class for a grade..i need an "activity" or 2 i can do with this.

o..nd y dont u just put pi on the outside of the integral nd multiply it after the integration? just a suggestion..works 4 me.

[chalittlefield]

you are a life saver!

[EmpressRan]

OMG you are a freaking lifesaver. Why couldn't you be my calculus teacher?! I may actuaolly pass calculus with higher than an 80 now. THANK YOOOOOOOOU! <3

[Jassmine1791]

Thanks for the uploads. :]

Your Videos have really helped Me.

thank you!!

[patrickJMT]

you would have to find points of intersection, justify which one is 'farther away' from the line you are rotating about

[HeadofSpringfield]

accidentally pressed spam to 500stephen500's comment, I actually wanted to know the same thing

when your only given equations, how do you know which one is inner and outer radius??

[500stephen500]

how would you know which is the inner and outer radius without a picture, only equations?

[patrickJMT]

see my comment if u are still interested in volumes of rev.

[mszpbshiix]

you're AWESOME

thanks for being a lifesaver/gradesaver

i could pass calculus just watching your videos!

[ruleas2kings]

why are you better at explainign this then my shitty calc 2 professor

[ctownstang]

Thanks man. Your videos are really great. Im taking calc. 2 but my teacher goes over everything so fast, sometimes I get lost. I wish she had a pause button like youtube.

[dapoochiman]

i feel bad cuz everyone else learned this a month ago, apparently, according to the posts, and our BC class is just finishing this up =X

[patrickJMT]

well, people take topics in a different order, so i would not worry so much about it

[mofomaniax]

I learned more watching this video than in my AP calc BC class. Forserious.

[mjosp]

You are AMAZING

[fauszayas1]

Great job dude... Keep up the great work...

[missroxysurf]

You helped me out so much, and at the last minute too! Wish I would have come across your videos sooner. Just in time for finals though :)

[patrickJMT]

yep, better late than never : )

[FZXPhd]

patrick you might be saving my calculus II grade. thanks for all the videos, awesome explanations!

[patrickJMT]

you are welcome! just give them good ratings and tell others about them! : )

[bboyhfeet]

You saved my life, thank you.

[DJFONSO1]

Nicely Done!! Better than my calc 2 professor :)

[patrickJMT]

THanks!

[theonlyrealshark]

Thanks!

[Waranle]

Thank you alot! great video