Calculus 3 Lecture 14.6: How to Solve TRIPLE INTEGRALS (Along with Center of Mass and Volume)
Calculus 3 Lecture 14.6: How to Solve TRIPLE INTEGRALS (Along with Center of Mass and Volume): What Triple Integrals mean and methods of solving them. Also discussed is the idea of a triple integral representing mass and volume of a 3-D region. Center of Mass is also covered, but more examples in 14.7)
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That moment when you realized that you'd rather watch a free video thats 3x longer than your college class to which you've paid a shit ton of money for.
I was looking at my phone when he said "look at the board, stop what you're doing and look at the board" so I put my phone down and did what he said.
"Yo dawg, we heard you like integrals. So we put integrals inside integrals inside integrals so you can integrate the integration while you integrate." - Leibniz
@theshoulderofgiants
3 жыл бұрын
Newton**
@anthroporraistes_
3 жыл бұрын
@@theshoulderofgiants Leibniz***
@nebaashibruce8793
3 жыл бұрын
dis sound like a yaad man mek dis comment.
@gregtroll
2 жыл бұрын
Turducken…
@canman5060
2 жыл бұрын
I integrate 1500 times in my Phd Maths Thesis !
30:00 Z-simple 40:30 Ex 1 47:00 Ex 2 58:00 Ex 3 1:19:16 Ex 4 Finding mass with p(x,y,z) 1:36:00 Ex 5 Using Y-simple. Example when you are not sure which order the upper/lower bounds are 2:02:55 Ex 6 2:36:22 Ex 7 3:02:00 Ex 8
@invincible2914
2 жыл бұрын
3:15:00 center of mass 3:22:52 Example 9
@receperdogan9285
2 жыл бұрын
thx for helping
@deemgr7
Жыл бұрын
Thanks
Damn it, why couldn't the video be 2 seconds longer.
@Nicoder6884
8 жыл бұрын
You mean one second?
@gwaites6329
7 жыл бұрын
hha yea either 2 seconds longer or 1 sec shorter, or even 5 seconds longer so we get 3+33=36
@gwaites6329
7 жыл бұрын
X D go to about 1:15:42 and put at .5x speed X D sounds like a high californian surfer
@gwaites6329
7 жыл бұрын
1:15:39 *
@tlhomotsemoteme2423
4 жыл бұрын
G Waites lmfao
I owe my A’s in calc 1, calc 2, and now calc 3 to professor Leonard. Professor you are a fantastic teacher and have set the bar for all professors across the globe. Thank you for being an amazing human being and being their for me in my upper division math. I honestly don’t know where I would be with out your videos.
@hassanaftab6219
3 жыл бұрын
Which book Professor is using!
@irenewilliams5145
2 жыл бұрын
That's cool
@evanjones9602
11 ай бұрын
@@hassanaftab6219 Early Trancedentals, James Stewart
THE LEONARD!! Simply awesome. Math isn't so bad when you've got the Leonard in your corner. It's actually kinda fun! Thanks Professor. Not too many people can do what you do.
@masoomaibrahim3893
2 жыл бұрын
8th
@upriiserii5895
2 жыл бұрын
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@RakeshYadav-tj5os
Жыл бұрын
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my university goes 3 times as fast as professor leonard but 20% as deep. thanks leonard! :)
@Anigmus_
2 жыл бұрын
@@stillfranc that was pretty good
@johnestrella4223
2 жыл бұрын
@@stillfranc o
@bawol-official
2 жыл бұрын
Same here, its par the course though for most places that arent prestigous or private schools. Thats not to say you cant find them. The best math teacher ive had in my life was taking a College Algebra course at my community college, flunked math all throughout highschool and passed with an A. Changed my major to Computer Science just so i could learn more math while staying true to my experience in tech. Theres Prof. Leonards out there its just a matter of chance.
@mplsboi1990
2 жыл бұрын
@@stillfranc you win the internet
@naoremningthemton5316
2 жыл бұрын
@@Anigmus_ ,
the fact that we use the same textbook is sooo helpful. For anyone wondering, it's Calculus Late Transcendentals 10th edition by H.Anton, I.Bevens and S.Davis.
@sterlingmillhollon2520
Жыл бұрын
It is also following closely the "Calculus" 10th edition by Ron Larson and Bruce Edwards
@evanjones9602
11 ай бұрын
Early Transcendentals 8th edition too
You don't know how much you helped me,you literally kept me away from anxiety,depression,etc..thanks a lot may God makes your dream come true🙏🙏🙏
This guy saved my semester. My calc 3 professor goes so fast during class that I don't understand the notes I take.
@keylanoslokj1806
2 жыл бұрын
Yeah cause colleges try to give you overly compact knowledge in just 4 months
@mewos838
2 жыл бұрын
@@keylanoslokj1806 my college: in 3 months :_\
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@miguel1502009
3 жыл бұрын
Walter Lewin is your guy
@joeyGalileoHotto
3 жыл бұрын
Michel van Biezen is a good option
@sergeirachmaninoff6397
2 жыл бұрын
Walter Lewin is as good or even better with his demonstrations! Regarding explanations they are on the same level.
@Lena-zn4re
2 жыл бұрын
Looks like I saw this comment just in time, physics is absolutely screwing me over
@ritesha8050
2 жыл бұрын
sir Walter Lewin is a physics god. There is no way you cant understand.
Love this man, can’t believe I didn’t watch him until now. Would’ve been great for calc I and II
I got a 97 in Calculus 3 thanks to you professor!
@guitarttimman
4 жыл бұрын
pretty good buddy.
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2 жыл бұрын
damn bro
@kalebscott282
2 жыл бұрын
I'm here because I'm at a 67% lmao
@canman5060
2 жыл бұрын
Genius !
@johnathantran1101
Жыл бұрын
97 seriously! you are a god's child
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Far more informative than my math professor and actually entertaining to watch, I just learned more in this 3 hours than I have in the past 6 months of calc, Thank you!
I got an AA in calculus 2 and thanks to your videos. I had a tough time while I was doing calculus 3 as calculus3 videos were not uploaded. Thanks very much for making it available. With this videos I might be thinking about retaking calculus3 to make a better grade.
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Damn I have been using integrals for years and never really understood the concept behind triple integrals. The way you explained how single, double and triple integrals are used at the very beginning was perfect.
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Wasn't fully understanding triple integrals for my test in 2 hrs and I *NEED* to pass Calc 3 to transfer. This helped a lot, since it's a lecture
I spent hours trying to understand double and triple integrals. Literally an hour into his videos, it all makes sense... Thank you so much!!
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video 33:33 long (almost 33 secs), 333K subscribers, 3 integrals, 3D regions, Calculus 3, I'm scared!
Would you ever consider putting up some kind of mock up of your exams with their answers? I feel like your tests would be much more challenging in the right way than our teachers.
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I’ve been scrolling KZread for so long I ended up here. May god bless my soul.
you are really good!!! way more good than my professor!! loved your teaching style... lots of love & keep it up!!
Dear Professor Leonard, Thank you for your explanations. greetings from Slovenia and Turkey!
I want to say, thank you for this. During this time it is extremely hard to find help. This help me to the core. Z-simple. I have a great insight on integrals. I wish my professor was like you. You're amazing and handsome too.
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.....and also THANK YOU FOR NOT SKIPPING STEPS!!!! You rock, bruh!!
Professor Leonard, thank you for another fantastic and lengthy video/lecture on How to Solve Triple Integrals(Along with Center of Mass and Volume) in Calculus.This is another tremendous amount of material to absorb, however the way each example is explained is incredible. In Mathematics, the Center of Mass is explained really well in comparison to other courses in Science and Engineering.
Single integral - area under f(x) (2-d, x,y) *OR* mass of a straight line (1-d) (??? investigate/review) "Distance along x-axis" 14:38 Double Integral - VOLUME under f(x,y) (3-D) *OR* mass of a thin plate (plane region) -thin- flat (xy-plane) Trippe Integral - Some measurement of region under f(x,y,z) (4-D concept) *OR* Mass of plate *with* thickness (cube, or surface) 14:58 ... Tripple integrals create a region just like double and single integrals. However it is defined in 3D so it a surface of x,y,z (cone/spike). Now take the mass density of EVERY point on this surface, and it tells you the mass. 18:00 Tripple integral defined S as between two Surfaces. 24:20
professor leonard, you are an amazing teacher. my current calc 3 class sucks, and i understand everything so clearly thanks to you. thank you so so much!!
Helped me understand Electrostatics! Thank You Prof Leonard!
I've always wanted to say that I do not know how you do it but your English is so clear. I come from Polish and my English is at the level of understanding and you listen to great! You are an excellent teacher. Even the language barrier does not spoil the content. Thank you for your videos and knowledge. Yours faithfully
@chandranichaki9580
2 жыл бұрын
Watch the latest video of wishing happy new year in the language of Mathematics kzread.info/dash/bejne/nqWKp8mPlcSadMo.html 😊😊
Amazing professor this guy. I passed Calc 3 a few years ago and it is so neat to go back through this stuff. Great work
@f.b.i1068
Жыл бұрын
Why do you have to go back through it again?
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Literally better than any math professor has explained anything in my whole time at university, I'm so bugged I found this channel in my last semester before I graduate. If I had to give any stem majors advice it would be to watch these videos.
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Happy birthday Leo :D Thanks a lot lot for this videos
It's all about identifying what's bounded and what's simple. Good video.
i spent the day studing this video, easy to understand. Thanks professor Leonard, obrigado!
You are possibly best Cal 3 Prof!!!
Such an amazing instructor. Thanks
professor leonard is a 4d function of mass density of education. my brain gets smarter as this video goes on.
@ILikeWeatherGuy
7 жыл бұрын
i.e the mass density of the correct electrons in place in my neurons get denser :D
Thank you!!!!!! I've been yelling at my book for 3days and asking it "how many dimensions am I in???!!!!!" (3 or 4????) this helped a lot!!
this video really helps me a lot in understanding what triple integrals represent and mean, thanks a lot !!! ❤
more i watch professor leonard the more i absolutely love his teaching style. so many amazing examples with clearly outlined definitions.. also he sometimes smiles just like homelander after cracking a joke lmao Cant wait for his linear algebra series! I need it
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This was amazingly helpful. Thank you!
hi Professor Leonard, thanks so much for your videos. I use to love math, i even competed in the mathematic olympiads and managed to get second place. But when i started engineering I hate math and barely managed to pass calc 1 and failed calc 2. But after stumbling across your videos im starting to enjoy math again and am kinda sad that i have finished all of my math courses for my degreee. Thank you so much
crushing my calculus tests easily after watching this far.
Give you credit sir ... You explained what many professors doesn't do ... They just teach for exams not for beneficial use and right applications
this was a great lesson. learned so much. thank you
ابداااااع ... ليت بعض الدكاتتره يتعلموا منك ..
I wish my calc professor explained like this and was good looking as well. I would never miss class ever lol
@tripp3468
7 жыл бұрын
racist
@user-lc6jq1hi1r
3 жыл бұрын
"good looking"?? what? are you going to college to marry your teacher or to study?
@vaiterius
3 жыл бұрын
@@tripp3468 how tf
@astrar7
3 ай бұрын
?????????????/@@tripp3468
Z-simple - 30:00 Ex 1 - 40:30 Ex 2 - 47:00 Ex 3 - 58:00 Ex 4 Finding mass with p(x,y,z) - 1:19:16 Y-simple. Example when you are not sure which order the upper/lower bounds are - 1:36:00 Ex 6 - 2:02:55 Ex 7 - 2:36:22 Ex 8 - 3:02:00
Professor Leonard, what book does your class use? Thank you for this great video also!
i love u professor leonardo toooooooooooooo muchhhhhhhhhhhhh.thanks alot am a first in calculus in our class .from ethiopia
You are amazing sir,.. you helped me alot, simply more than enough...
U r awesome!!!!! Thank u mr. Leonard.Its really helpful to me.
give this man a raise
What a wonderful lecture !!! Ty sir
thank yoy so so so much ❤ l'm watching your videos from the first second till the final second l can't tell you how much you helped me l really appreciated ❤ much love for you professor ❤
Man! This guy is great at what he does. Makes me wish I could go back to school.
+Professor Leonard - I am so thankful for all of your time and incredible teaching methods! I have been using your videos for a couple years now, and they have been the most valuable resource for me. Whatever we are learning in class, I always understand conceptually and how to solve the problems 100% more effectively after watching your videos. Thank you, thank you, thank you! Side question- We are wrapping up the semester with Line Integrals, Parametric Surfaces, Curl/Divergence, etc. - Will you be covering this in your class soon? I want to watch your lectures so I can study for my final!
I wish I had a professor like this when I was at the University. This was very interesting. I graduated (msc engineering physics) 17years ago and by chance stumbled upon this and I just had to watch the whole thing. Awesome example of a great teacher, focussing on understanding so it is much easier to understand what is happening instead of just learning integration techniques. Thanks for sharing!!
You know what I love about Professor Leonard's teaching, he squeezes a reminder of past vital concepts and ideas from previous topics. So if you learned, but didn't fully understand something entirely in i.e. double integration, you wouldn't need to go back to his double integration videos; he catches you up on the go. Like the level of in-depth teaching is far beyond what any of my past/current lecturers do, so coming from any other lecturer to videos literally fills those knowledge gaps.
Dr. Leonard, Thanks so much for the great videos. What happened to lecture 14.5. Apparently, this a key video for understanding 15.6, but I can't find it in the playlist. PLEASE ADVISE.
Thanks a lot, you are a very good teacher
Bro first video and with In The first five minutes I can tell I wish I had you as my math teacher. So helpful.
you are great sir you are very fundamental ...love you and thank you
Thank you. Thank you. Thank you. I am yet to see your teaching style matched. Much appreciated from Zambia.
I laughed when he said "Y, no I mean por qué". Hahaha.
in calc 2 now. I can't even express how much I'm looking forward to calc 3.
I just use Geogebra when I graph this stuff, haha. Perfect program for 3D graphs, and you can graph curves as well if you plot them as parametric equations.
At the beginning of the video (around the 6:50 mark) , he's talking about the ambiguity of a 4-d equivalent of volume. I wonder if you could express it as the change in displacement experienced by free space over a given time period. Maybe that's way out in left field, but it kinda works in my head.
I wish you were math teacher..............before I come here...........calc 3 was like nightmare for me.......thanks a lot sir...........I looooove the way you teach.....
Thank you so much. You are a hero!!!!!!!
Yesss thank you so much for this video!
There are two versions of calc 3 in my uni and I am taking the easier version suited for engineering and most business students. But these vids are for the harder version, so I am going above and beyond on such vids. I only need an average of 1.52 attempts to solve a calc 3 webwork problem correctly, but for calc 2 without Leonard it was above 3.00. And now I have calc 3 as the course to pull my grades up. So many of my friends are struggling but I am breezing through.
"I'm 83, I age really well. Strick diet of quinoa and steroids. I'm joking don't take steroids they do weird things. Ask my uncle he was Mr. America." --Professor Leonard what a golden quote...No way is your uncle Gary Leonard!!! LOLOL
@ProfessorLeonard
6 жыл бұрын
Hahaha, love to have fun!! But yes, Gary Leonard really is my uncle
Super helpful - thanks!
He wasn't lying about Gary Leonard. That is awesome.
I wish there was a professor like you for linear algebra as well
@Peter_1986
Жыл бұрын
He will start Linear Algebra in the near future; he said that in his most recent video on this channel.
Estou gostando muito dos seus vídeos, dando like em todos.