Volumes of Revolution about Vertical Lines Using Washers

[TennisPoet]

Hey PatrickJMT I know you have a 10 min limit and whatnot, but could you please put the answers to the problems you don't solve all the way through in the description or something? Just in case I make a stupid mistake, I'd like to catch it to make sure. The first one I got (1023pi/5) and the second one I got (17pi/15) Thanks.

[CoconutMigrating]

I have a question here. Wikipedia says that when the axis of revolution is not the x or y axis, you should take the (line - equation). Here you took the (line + equation). Why is this?

[patrickJMT]

@CoconutMigrating it depends on the geometry of the region and depends on where the line is....

[Kuffly]

asdfjkl; OHMYGOD. Thank you sooo much. I've been having a hard time with the volumes of solids of integration when the axis of rotation isn't the x or the y axis. It suddenly seemed all so clear when you drew the perpendicular lines and stuff! Awesome videos, by the way! Thanks for helping us out! :D

[ICarnag3I]

Do you always differentiate with respect to y when going about vertical lines? I got points off

[patrickJMT]

@ICarnag3I it depends on what method you use

[ICarnag3I]

@patrickJMT say it's about x = 2, using cylindrical shells. I got points off my exam for differentiating with respect to y.

[patrickJMT]

@ICarnag3I yes, if you use shells it should be with respect to x.

[patrickJMT]

@ICarnag3I in this case at least

[socerplayer23]

nevermind forget what i said lol i feel stupid now.

[socerplayer23]

i thought you were you using horizontal lines.....im confused

[TheAnonymousify]

For some reason there is a really annoying buzzing noise in this video.

[patrickJMT]

@TheAnonymousify old video, crappy mic i guess

[DonenDone10101]

Patrick, I'm having a dilemma finding something. All of the examples of solids of revolution involve only vertical and horizontal lines. I was wondering as to how you would go about rotating a graph about a slant line such as y=x. The only thing I can think to do is rotate the graph, before integrating, such so that the axial line becomes the x or y- axis. Is there even such a problem, or am I just searching an ignorant idea? Please help. Any help is much obliged. ^.^

[patrickJMT]

@DonenDone10101 i do not know of a formula off the top of my head, i would have to derive one.

[tombey12]

Thanks buddy! Learned so much from you lately

[supersal001]

Fuck you ads

[supersal001]

@supersal001 unless all add rev goes to patrick...come at me ads

[patrickJMT]

@supersal001 a large portion does actually. it is why i am going to start working full time on making videos starting next year. the ads are why the videos exist - someone has to pay for all this free stuff.

[xxbia]

@patrickJMT I wish I could be a full time YouTuber! :) Sounds like a fun way to make a living.

[pinkfuzz0609]

Your instruction is spot on. Calculus baller status.

[serpensortia01]

i think you forgot to write dy in that general formula at 1: 48

[MultiMoe91]

hey patrick thanks for the video of Volumes of Revolution - Disk/Washers Example 1 ..

i have a question which is bugging me..

in the first example you wrote its rotated in the x-axis.

can't we use the formula pie intergal c to d [g(y)]^2 ?

i'm kinda confused when to use it exactly

thanks :)

[hiphop1andrbbabe]

I WISH I SAW THIS VIDEO BEFORE MY ASSIGNMENT! BRILLIANT!! UR WAY BETTER THAN MY PROFF

[SirDamienQFox]

Are you an INTJ patrick?

[patrickJMT]

@SirDamienQFox probably

[lecoupdevie1]

On my first calc midterm I got a 53 (which was a B after the curve). I discovered these videos two days before the second midterm and I got a 90 (93% after the curve) Now here I am reviewing for my final tomorrow! Thanks for all the help! Do you have physics videos?

[PhanatixDDH]

You are the Michael Jordan of Calculus. There for me in the clutch!

[patrickJMT]

@PhanatixDDH yea, but mj seems to act like a douche bag anyone talks to him. i would rather be someone else : )

[11011111011]

@patrickJMT kobe bryant

[Busterrhymes6]

You are the greatest! If only my professor would explain things simply like this. Thank you so much!

[QQHeatherx3]

Thank you very much!

[chuckifubuck]

thank you so much for making these videos. they helped a lot.

[H4lo450]

Dude i'd appreciate it if you helped me out with this problem. Region bounded by the graphs; x=y squared, and x=4. Rotating about the line x=6. Thanks.

[Chimpalimp1001]

May I suggest using different sound recording software, or a headset mic. The feedback gets irritating. Very thorough, awesome stuff!

[patrickJMT]

this was an earlier video... most of the sound issues have since been fixed.

thanks though.

[monkeykingy]

this is good, but the sound is really bad and annoying. I had to mute it to watch it.

[Xinoutorah]

Question, what if you are in a different quadrant? I understand how to do them all in the first quadrant but looking over a past test I don't see why when you revolve around the line x =1 (for example) you end up subtracting the one instead of adding it if the function is x=-sqrt(1-y^2) ---placing it in the second quadrant)

[scarykidbryan]

If I get 100% on my Math 9B class at UCR tomorrow, I'll paypal you money!!! I'm not even joking. These videos helped a lot.

[MrMarieBiscuit]

thanks a bunch man gosh ... i needed this :D !

[dmsfid7205]

I can't say thank you enough!

[milkcar92]

what about translating the graph to integrate it?

[cLorproductions]

Like many others, thank you so much.

Your videos are truly helpful.

Once again, THANKS!

[omgcollege]

I could not understand this concept for the life of me, and your video has definitely helped me prepare for the AP exam. Thanks sooo much!

[xylokid4]

yes! i couldn't find this one at first, and i figured it wouldn't be here. But you put up vids of everything. You know you're the greatest right?

[patrickJMT]

haha, not quite : )

glad it helps though!

[Ren520]

u forgot dy on the first one heh

[zakria15]

thanks a lot ..that helps me a lot in my final

[balasubramanianzoom]

you da man