Longer Version - Volumes using Disks/Washers

[YASSIN0500]

i love u man

[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!!

[saturdayismonday]

and YOU are the reason that i got a 95 on my ap calc midterm:D thankyouuuuu

[patrickJMT]

@saturdayismonday happy to help :)

[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!)

[gthivs]

Thank you so much!

You are AMAZING!

[colombia037]

very helpful!!!!! THanXXXXXXXXXXXXXX

[rtojj]

When people ask me what teacher I had for Calc I give credit to my real teacher patrickJMT I think of my professor as an assistant that gives me notes for when I watch your videos

[jennygallery]

why is it i spend an entire two hours in class completely confused as to how to do these problems, and i watch 15 mins of your video and understand it completely. my university definitely needs you as our calc professor!

[TheDaisygirl5]

So you helped me pass my calc 1 class, now lets see if you help me pass my calc 2 class! Thanks for posting this up. It cleared up everything!

[Canada9318]

My Calculus study pattern:

1) Take notes in class

2) Read textbook

3) Watch PatrickJMT

[patrickJMT]

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

[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.

[patrickJMT]

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

[Canada9318]

@patrickJMT Yep, people can be taught all they want, and can try to learn all they want but the knowledge isn't theirs until they actually apply it.

[butofcourse22]

Thanks so much for the help. Like a TA on the internet

[philster00700]

Also, plural of 'radius' is 'radii'.

[philster00700]

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

[Fiendlord9]

Wow, this is amazing

[xshanayy]

" a little confusing".... are you kidding me?!!?

you make CALCULUS MAKE SENSE

throw out my text book, my professor, they make NO SENSE all i need is your videos to get an A <3

[patrickJMT]

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

[PwnagePC]

@xshanayy I thought the exact same thing, "a little confusing". Made me feel special for about 5 seconds, lol...

[AceAites]

THIS IS AMAZING. THANK YOU. And whoa, 21 minutes. Your videos so long that Youtube had to make an exception ? ;)

[FuckTheRickrollers]

why couldn't I find this at the beginning of my AP calculus course T_T....At least I can use them for the AP test and college :D

[Angelgrrl04]

How do you know which axis to rotate your function around? Or is it given?

Because I noticed that there are few other videos you have with somewhat similar graphs, but it's rotating around the y axis.

[URBNSpice]

So for Disk/Washers rotating about xaxis is dx. And for Cylinders rotating about the xaxis is dy? I thought it was the same for the past hour!

[S3aW3ed]

Thanks Patrick. You helped me understand a concept that puzzled me. Keep up the videos :)

[11011111011]

bro, i should just watch your videos instead of going to class....

im a bit confused of functions in terms of y, so like x=y^2, then rotating it around y axis and x axis,

thanks again for the help!

[djmdogify]

PatrickJMT has a bigger shrine than Buddha.

[MzVixen05]

The way I love you right now... at 1:52am not even my bag of Lays is comparing to the things you're making me feel... I just may get that A :P

[NguyenEmpir3]

For the rotation about -3 or "a number", is there a specific formula or something to add or subtract

on problems like B, I always mess up with (3+ root x) and (3- root x)

[myandroidvideo]

You are awesome

[TheMikeGClark]

Is it bad that I pray to you before calc tests

[patrickJMT]

@TheMikeGClark hahaha, that is hilarious. i do not think it is so bad. uptight people might though. maybe you should bring a picture of me, light some candles, and do a little prayer in the corner before class and see the reaction... : )

[Parkyy16]

@patrickJMT This gave me an idea. I'll do exactly that. Hell, people already think I'm weird. I don't think one more strange thing would hurt :P

[backhandable]

@TheMikeGClark You should go the full monte and concider a small sacrifice

[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

[Guntheman]

amazing stuff. thnx.  =)

[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!

[manlyman6392]

your the shit man. mad respect

[serpensortia01]

thanks for the videos

[josephtanaya]

thanks!! the ads is really annoying. it pops up in the middle of your video

[hectorterrero]

Dude,I'm in college studying Civil Engineering and I watch all your Integration Videos to study for my calc exams, mind you i got to RIT

[MegaEvolym]

thank you very much . .you really make it simple in a way that even I can master it in a simple way . you are better than my teacher

[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!!

[illusionized93]

how do i know whether or not to use disk/cylindrical?

[koliupy]

Dude you're awesome... thanks for all the help.

[DemonPacman]

You're doing a great thing for struggling students man. Thanks PatrickJMT.

[bryan91292]

you have very good penmanship and you even draw proportionally, which helps me very much.

[SkyHighImpalaz]

ugghh tell you tube cut out the commericals im tryin to learn!!!

[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

[NovaSazoku]

there's a really annoying high pitched noise in the background. but thanks for all the help, i was looking for something like this

[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)

[pr123inga]

thanks!

[pr123inga]

You are GOD. You have helped me with everything! I mean I got a 13% on my calculus quiz b/c I literally had to be taught everything about this section. You did that with this and like a bunch more videos. I end up having a test on the same material and I got a 100% b/c of you.

[patrickJMT]

@pr123inga congrats : )

[SolitaryAngel917]

Quick question, my calc teacher is testing us on this and he's not letting us use a calculator. Would it be correct to just place the pi sign next to my answer after I do the integration?

[patrickJMT]

@SolitaryAngel917 yep

[iSt3phNgx3]

how do you rotate the functions stuff around a vertical line? like x=3? can you make a video on that? :D thanks!

[patrickJMT]

@iSt3phNgx3 almost positive there are videos about this

[iSt3phNgx3]

@patrickJMT thanks for answering me :'D and YES i found the videos xD

YOU ARE SO AWESOME!!!

[bubblelink47]

why can't my calculus teacher be this good :/

[dy2451]

Thank you sooooo much. This stuff is so simple now thnks to you. Keep it up Patrick!

[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!

[cortesjosed]

I DONT EVEN CARE ABOUT THE NOISE =D

[mas3rm1nd]

great video but my ears are going eeeeeeee :P

[drmaqueen280]

thank you SO much!!! :')

[pepekong]

Too bad human cloning is not yet possible, cloning Patrick to teach on every school there is would make life a lot easier.

[aaronmhahs]

Please come teach at UCLA haha

[cpxjimmyboi916]

Hi I Love These Helpful Videos. I Have A Question With A Problem:

How Should I Start With: y=x, y=e^(x-1), x=0

[Metalgod89]

Oh man there is a horrid sound in the background.

[xsqueetzzz]

@Metalgod89 its so bad

[brettmfm]

Your a savage!!!! keep up the good work!!

[ramshambo2001]

Thank you very much. Your made it much more clear then my Calc 2 teacher!

[mikolbeckwith]

So just to get this straight when using the disk/washer method and rotating around a horizontal line we integrate wrt x and when using the shell method to rotate around a horizontal line we integrate wrt y?

[JoshBuntu]

you shall inherit the earth

[patrickJMT]

@JoshBuntu ha, that sounds like a lot of responsibility

[cyborgninja74]

I have one problem. I don't know how to graph the basic functions, I mean I do have some ideas of how I should graph it. But is there any way that I can do this problem by not graphing it? I heard we can plug in numbers into the function to see which one is the top function or the bottom function. Can we do that instead? Without having to graph the whole thing, just having a mental visualization?

[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

[Glenn08CRF]

Great work Patrick. Thanks!

[stevenmcconnon]

wow you just helped me understand this

[americanjubilee4]

YOU ARE AWESOME!!! Thank you so much for this!!! It saved my life in Calc 2!!!!

[TheCoolfez]

this is awesome. I hate how I am spending $2600 for calculus 2 this summer and I am learning nothing in class. And I learn more watching youtube videos

[silentc1015]

Thanks a lot for the video. I just had this lesson today in calculus 2 and didn't really get it. Your actual drawing of the inner and outer radii (is that plural for radius?) made it very clear. Thanks again!

[themraluminum1980]

Don't fogget about it! 5:24:)

[CrazyIemon]

wow...if I had seen this video before...

*Takes deep breath*

Well, at least I managed to see it before my final. Hopefully I'll be able to do well now!

[qumanramos]

@ 4:35 Blooper....

[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?

[flaco954]

I would love to experience your actual courses. You make things look like clockwork. Thanks again!

[koreahiho]

Shouldn't I have the same values for all of three? (a,b and c)

Since the empty part (from the rotating axe to the graph of the functions) is negligeable?

Or am I just being stupid...?

BTW, u r awesome!!!

[emerica2225]

@koreahiho you're just being stupid, when you change your radius you change your shape!

[YOitsNat]

Thank you so much this is great!

[guo0]

thanks!

[Balkance]

I'm sorry but I didn't seem to find an example showing the Washer method around the y-axis... maybe it's not as confusing as I think it is but umm... yeah.. thanx for your help on the rest though..

[Smarkand28]

thank you so much, these have been very helpful on my test

[youknowho90]

YOur videos are awesome!!! Thanks you so much!

[Elite17xx]

awesome video

so well-explained that even a high school student like me can understand.

thanks soo much :D

[ravensrock86]

very informative video. the only thing i can think to complain about is the annoying buzzing noise in the background. but regardless, thanks for the tutoring sessions!

[crystalshayblack]

Thank you very much. I'm taking Calc II and this is an amazing review.

[237160]

dude out TA has been trying to teach me this for the past week.

i learned it the first time i watched this video.

you are an AMAZING tutor. keep up the good work man

[amrichbiatch]

dude this video is best ........ keep up the good work

[MMMETALL]

Left handed for the win. Only way to be.

[Xinoutorah]

Apparently more people should be left handed, but society forces people to be right-handed.

[BlackHatProductionsx]

badly said, they are alot of factors invovling left/right handed attributes, not society as a main cause.

[Xinoutorah]

@BlackHatProductionsx Poorly said you mean :)

I didn't say it was a main cause... "badly" assumed on your part ;) Stop trolling and go do something productive.

[NicoThR]

thaaaaaaaaanks very much!!! this is so usefull

[rryking]

brilliant stuff. So basically, it's washer method when there's 2 f(x)'s, and disk when there's 1 f(x) rotated about an axis? Or no? Also, which method gets multiplied by π and which is multiplied by 2π? Thanks

[dayoungn2]

disk/washer pi

shell 2pi

[dukehoops]

This video was extremely helpful, thank you

[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?

[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 : )

[mikestephan520]

AMAZING VIDEO...as always. i just have one recommendation (such a problem appeared on my test)- show how to rotate the area between -x^2 + 4x and the x-axis around the line y = 5. someone explained to me afterwards that you have to still use the outer radius/inner radius thing. or maybe you can say that the outer radius/inner radius idea always applies, just that when your rotating that same area around the x axis, the inner radius is essentially 0. i think that explains it the best.

[cutedude22]

Is this calc 2?

[TedGreyfox]

Most places include this in calc 2, which is usually single variable integration (atleast around my area).

[howdydutt1e]

wowweewowwee thanks mann

[vlaplayer]

This makes a lot more sense now. THANKYOU.

[stevnpham]

You sir are a god for all of us students who have hard to understand calculus teachers. Thank you very much =].

[patrickJMT]

my pleasure

[mistuhsparkles]

Hi steven, it's brian

[chrisortiz713]

Sir, your videos are superb. I am greatly indebted to your services. I wish you prosperity. No seriously, you're awesome. You alone are saving america's youth from failing their calculus classes. Bless your heart.

[patrickJMT]

all except the one's in my classes... : )

i am glad you find them so useful and of good quality : )

[osiris392]

no kidding my calc teacher is terrible. i havent learned one thing in his class all year. and it's already the 4th quarter so im down and out. also what is the real world use of calculus. all ive seemed to learn is that these 2 random functions just ahppen to work out perfectly in whatever topic we're on like integrals. to me it seems like i signed up for a class that's nothing but riddles and math coincidences.

[Luciana08E]

I get it now, thanks!!!!!!! Violent example? ahaha.

[patrickJMT]

why violent? : )

[Luciana08E]

you referred to rotating the graph of sqrt(x) as a violent example because it resembled the tip of a bullet. ^u^ !! ...... .. .. ^u^

[patrickJMT]

ahhhh ok : )

[BigT4313]

Thanks alot man, this will definitely help for my midterm on Wednesday! Kind of a dumb suggestion, but could you make a video on basic graphing?

[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.

[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

[ILagAlot]

Just learned this monday, thanks for the review :O

[beneaththeabove]

Thanks again, well explained!...

btw, what university/college did you go to?

are you still at uni/college?

I'm guessing you did maths..lol....

5/5

BTA