Triple Integrals, Changing the Order of Integration, Part 3 of 3

[@scottmullen5829]

"You can always plot points if at this point you're losing your mind." Made me laugh pretty good

[@Sam-fm8eh]

You explained it graphically without algebraically rearranging inequalities like my lecturer which is exactly how I think! Thanks so much!

[@claireabella1]

"shoot a bullet through the tent... hopefully you're not there.." idk why i lol'd so hard

[@zombie-blood-490gaming5]

hahaha

[@101pokemasters]

I will never understand why professors will deliberately skip over the fundamentals to understanding this. They spend less time on teaching you how to set up the integral and spend more time on integrating without giving the student an idea of what the region looks like. Thank you for being human and spending the time to put together a well constructed explanation/video of something that should otherwise be so simple to understand when first being introduced.

[@bruceweng0305]

Thank you sir! My calculus II class apparently doesn't have abundant time for such thorough and detailed explanation for this. But for me this is really complicated. Thank you!

[@todwod]

Wonderful videos Patsy. Understanding my Polish Vector Calculus Professor where English is her 4th language, is a chore in itself, let alone understanding triple integrals. This is VERY helpful. Thanks!

[@palvindarchhokar9821]

I just went through your entire multivariable calculus playlist and it is awesome man! Thanks so much!

[@Samuelx123x]

Hi dude, just one little doubt, I think you misgraphed the region formed by the projection on the x-z plane, I mean it's a concave curve rather than covex one, I think you graphed , however it doesn't change the end result on the triple integral. I hope I explained myself well enough.. 4:30

[@greatcesari]

Samuel Arana Tessari Thanks for pointing that out. I was also thinking it looked more like z=1-x^2 or z=sqrt(1-x^2)

[@TheMyhrethomas]

I think this was a great movie, and you managed to show how it is possible to solve it with different approaches! Thank you :)

[@patrickjmt]

Glad that it helped you a bit :)

[@flarros]

Thank you for doing all of these videos! I was seriously lost before watching them!

[@fahadalazemi7930]

I just wanted to say thank you so much, you are doing a magnificent help. Thank you millions of times

[@Neiliean730]

"if someone shot a bullet in your tent hopefully you're not there" just made my day thanks pat!

[@echessbee]

Brilliant! I was struggling with the inner-most integral as it was never explained properly. Your surfaces/shadows analogies really drove the idea home in my mind!

[@smartyyoung7319]

Those two were actual on my HW lol

[@zombie-blood-490gaming5]

me too lol

[@wssz112]

why am i paying for college ??!!

[@bradwang3648]

Zheng SUn because once you got into your upper division class, there will be no tutorial video you could find on KZbin to teach you.

[@andrewdenterlein6447]

Thank you so much Patrick, this really helped make sense of everything concerning triple integrals bounds

[@CrimsonCorn1]

Very good and the thoroughness was what I was looking for. This helped a lot.

[@Twittygurl17]

Patrick, I appreciate your thoroughness! After watching all three videos, I'm much more confident about the quiz I'll be taking in 11hrs..lol Thank you soooooo much!!!!

[@AwkwardAdolescent]

So how did it go?

[@nidhishsharma9471]

@@AwkwardAdolescent the quiz killed him

[@oonniiigg]

Thanks!

[@HISTORYTODAY24]

Best explanation sir , I just love it .

[@patrickjmt]

yep

[@fedeottanta]

even if it's not my year's program I understand a lot of things, thanks you, the audio it's awesome!

[@thoranevans4832]

lol the question you showed at the end was the exact problem I was struggling with on my calc 3 homework that I looked up these videos to learn how to do XD

[@CodyShell]

that problem you issued out at the end is on my homework and it was a tough one!

[@OddRobb]

Thanks for uploading. Remind me in few years when I'm making millions and millions of dollars with my super-advanced degree and I'll write you a big check for your efforts.

[@keru1668]

Few hours before exam, lifesaver

[@berkaniinakreb]

love your handwriting en drawing skills, keep up the good work

[@gabrielfonsec]

I think it's to late to tell now, but isn't the graph of the region on the xz plane concave up?

[@vasquezg86]

This is absolutely great.

[@Aryan23329]

AWESOME VIDEOS ............ LIFE SAFER.........

[@islazheng4975]

It is wonderful! Thank you!

[@ow1ShinoXr]

great job although I think you missgraphed z=1-sqrt(x)

[@qvq17]

Thank you so much. This is one of my homework too... really helpful and very clear explanation. Thank you again :)

[@091MW2]

8:17 you can clearly tell patrick has had enough of this problem hahaha

[@chailatt3e]

Instead of a bullet through a tent or the sun's shadow, I imagined it as a projection of something to something. But I loved the sun's shadow haha

[@thatscoutisaspy]

For that final practice problem, I'm having a little trouble getting the bounds with integrating with respect to x first... I know that it's both x = sqrt(1-z^2) and x = 1-y but I don't know how that would be put into the equation. Also your videos are really great, subscribed.

[@christinaduan4238]

thank you soooooooo much Patrick !!! :)

[@Gauravani108]

Thanks for your videos, but I think you made a litle mistake by drawing the projection on xz-plane when you trace the curve that makes up the upper boundary which should be concave instead of convex.

[@xtasy2k7]

You appear to be right. His graph of z=1-sqrt(x) is incorrect.

[@lalithaprasad1662]

Luiz Almeida I get that the graph for z= 1- sqrt(x) is not correct. But then, will it change how we look at the "shadow" of the 3D curve on the xz-plane?

[@yrret1996]

Lalitha Prasad well the shape of the graph doesnt matter, as long as you see the boundaries and stuff

[@davidfransch]

Great explanations, thank you!

[@11SOCCERFORLIFE]

Excellent stuff.

[@ami1564]

7:09 "Have hope" and then I laughed a lot looool

[@chrisjuengling1983]

I get these processes suck but I could do (a-b)^2 in my sleep, and anyone doing calc 3 stuff should be able to as well lol. great video though! Extremely helpful in terms of visualizing the area you're projecting onto.

[@andrestamez7375]

Thanx pat really helpful hermano, have a good one

[@michellezhuang2483]

Hi Patrick, the equation z=1-(x)^0.5 should be concave down. I know it doesn't fit the shadow but it should be concave down.

[@liesalllies]

aw the end of this video got me nostalgic for youtube video responses haha.

[@Blobtheblobfish]

Thank you!

[@cxw2905]

This is really helpful!!

[@ProteinHammer]

You are a god send

[@motloungmatadiana4241]

thank you so much

[@Psychofear]

can you make some video's explaining this, but using polar coordinates/spherical coordinates/cylindrical coordinates? Thanks for the lovely analogies that helped a lot!

[@rockyguinto2325]

hi whats up buddy.. I have to say you did a very great job helping people that struggle with maths and for some people like myself who is quite preoccupied with daily stuffs yet whenever i do have spare time i race to my book and notes to learn math again- so i find your channel very very very useful and we are very grateful for that.. ^^ if could request you something bro is that, im working my way up to calculus here my man, hoping next year or 2 years id be able to get back to University,. thats why little by little i want to self-learn so if that time comes things would be easier.. hence asking you a big favor if you could just give me an outline on which of your videos to go first- that would make my learning be more organize. i mean, if i go algebra then trigo etc,. coz im embarass to admit that most of the playlist you created sounds all greek to me.. :( so there, bro if you could spare time helping a brother in need.. i promise you my engineering diploma. thanks. many many thanks.

[@jonathanmathurin4876]

hey im just a dropper by. if i were you i would go to the university site (the college you want to go to) and look up the syllabus's for college algera -> pre calculus -> Cal 1 -> Calc -> 2 -> Calc 3 in that order for however far you want to go. this will tell you which sections they cover and what the title of each section is. Example: Calculus 3 15.5 Applications of Double integrals. then you would go to one of PatrickJMT's videos of that title. For engineering you may need Differential Equations which is after calc 2. hope that helps man, and it sounds awesome that your going back and have taken the responsibility to prepare yourself. Keep it up and good luck!

[@marcoalban2105]

Amazing! Thank u very much!

[@VimalKumarSenthil]

Patrick you're videos are truly a lifesaver !!! I had this doubt , what do you do if the question does not contain a figure ?? And we have to form it using the given eqns . Any tips ??? Thanks a ton ...

[@restoreourhumanity2573]

god bless u bro !..kipidap..

[@121Boohbah]

thanks! I know it wouldn't change but I was just making sure I wasn't going crazy lol

[@HT-rq5pi]

these questions are easy if its easy to determine the projections onto each of the three planes...but I can't imagine how ridiculous things are going to get when we are no longer in rectangular co-ordinates.

[@marshmelows]

Thank you so much for the video, but I was kinda searching one with a harder solid...like when Z is between 0 and x^2-y^2...

[@donburde]

Oftentimes, when I have to develop these kinds of problems, I am not given any diagram or image to look at, just a couple of functions. Do you have advice for drawing/sketching higher order functions?

[@jpreciado93]

when integrating with respect to Y, when writing in the limits, do they not have to be the same variable for the lower and upper bounds?, or it doesnt matter because we will treat them as constants until we reach the approapiate dx,dz?

[@Felips0407]

use polar coordinates for that one, r^2=x^2+y^2

[@violinsheetmusicblog]

Hi Patrick! I was wondering if you could help me on a triple integral problem. I need to find the boundaries for this integral in respect to dzdydx. I watched these three videos on how to do this and they helped alot, but for some reason I don't understand this problem. It looks nothing like the others that I did. Anyways, here it is: int int int y^2 dz dy dx bounded by x^2+y^2=4 and 0

[@SweRaider1993]

This is all great and understandable and all but what about the actual function f(x,y,z)? So this is actually an integration with respect to four dimensions of some sort? I mean if you wanted to - let's say - calculate the volume here what would the function f(x,y,z) actually be? Just 1? I mean the function f is like in a fourth dimension that is dependent on these three variables; x,y,z. If someone could clarify that would be nice. Thanks.

[@michaeltruong405]

Wait for the most inner bounds, why isn't it from sqrt(x) to 0? (as opposed to to (1-z))

[@wangchul]

final exam countdown 12 hours god bless me

[@painfullyplaid]

perfect love the integration !!

[@MikelPesin]

thank you very much

[@121Boohbah]

isn't the 1-sqrt(x) suppose to be curving inward not outward?

[@AlvinIsChipmunk]

I love you!!!!

[@leredsock]

What do you do if you're only given the bounds of the solid, but no image or function?

[@jennifernouel995]

5:07 that sigh lmao

[@1966lavc]

now after considering all of 6 possible cases , as far as integration how do I no which one is easier to finish the problem?

[@Elyga.]

your vids are awesome, but the problem is that we wont get a diagram at the beggining, can you make a video or explain how to make a "base diagram" like your "tent"?

[@xiaoxiao0209]

you are amazing

[@A113Productions]

After integrating with respect to y, does the order matter when integrating with respect to x and z?

[@patrickjmt]

i would imagine the graphs would not be too difficult

[@Feanic]

So with triple integrals you have got six different orders or integration?

[@shehabalsiyabi6077]

Perfect

[@marshmelows]

Thank you so much for the video, but I was kinda searching one with a harder solid...like when 0

[@jonnnydeng8491]

awesome video:3

[@matthiasandersen3329]

Hi. In the practice problem in end of the video. I understand how to integrate dydzdx, dydxdz, dzdydx and dzdxdy. I can't get the integral right for dxdydz and dxdzdy. Anyone who knows how?

[@ICOD73]

Thank u Sir

[@SamoneModel]

You are awesome..! You help me review every test I have :)

[@MemoryDealer]

Hell yes.

[@HMSLion100]

the curve you drew at 5:16 looks like z=1-x^2.

[@gabe7996]

is f(x,y,z) given?

[@kevmarro]

Dear lord patrick this problem was 30 min long. Aint nobody got time fo dat!

[@dpt4565]

I wish I had a picture. Instead we get test problems like this: "Describe the region of the intersection between the elliptical of major axis 3 minor axis 1 and the unit sphere in the first octant" The video helps but it does not prepare us for the most difficult of problems.

[@zhenoob]

Has anyone tried out the little problem he gave at the end? I tried but I'm not sure whether my answers are right... :\

[@lordcasper3357]

I do not understand how you can write 1- sqrt x instead of 1 - y

[@pablitoooio]

Te amo

[@micky9217]

hopefully you are not there. hahahahaha. humor in maths, my teacher should learn that!!

[@LeHitman1]

I think your x-z projection is wrong... it should look convex not concave.. but it's not going to affect the integration.. just saying..

[@Mr_malo-d2l]

I don't know if anyone saw that but it was my light bulb turning on

[@JohnSmith-iu3fc]

sham!!! s o b

[@billycheung5114]

👍🏻

[@Diogo987321]

és o boss

[@shaneg31313]

it all makes sense until you don't have a graph and are forced to do what seems like voodoo inequality algebra

[@ricardoramos9939]

(i was not able to put the link)

[@engineerhere1061]

😍😍😍😘😘😘😘🕺🕺🕺🕺

[@edwardzhang1297]

4:40 this graph is literally false.