Calculus 3 Lecture 14.6: How to Solve TRIPLE INTEGRALS (Along with Center of Mass and Volume)

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Which book Professor is using!

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That's cool

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@@hassanaftab6219 Early Trancedentals, James Stewart

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He set the bar by being easy and incomplete? Come on man. Lol

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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.

[@lugia8888]

Pass. Takes him 3x as long to explain the same thing you learn in lecture. He also does not write complete theorems and chooses simple examples (simple examples are good for beginning practice, but eventually you need to move on to more technical/advanced ones). Decent guy to supplement material, but definitely not for replacing/ditching lectures.

[@junior5146]

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]

3:15:00 center of mass 3:22:52 Example 9

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thx for helping

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Thanks

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8th

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@@stillfranc that was pretty good

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[@bawol-official]

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.

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[@dagkouta986]

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]

It is also following closely the "Calculus" 10th edition by Ron Larson and Bruce Edwards

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Early Transcendentals 8th edition too

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Professor Leonard is the Textbook we must learn from You can have the textbook but if the concept is not well explained you won't enjoy the course.

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Now I just need a physics professor that teaches exactly like you and by that I mean easy to understand and wonderful at teaching.

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Walter Lewin is your guy

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Michel van Biezen is a good option

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Walter Lewin is as good or even better with his demonstrations! Regarding explanations they are on the same level.

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Looks like I saw this comment just in time, physics is absolutely screwing me over

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sir Walter Lewin is a physics god. There is no way you cant understand.

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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.

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I got a 97 in Calculus 3 thanks to you professor!

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97 seriously! you are a god's child

[@JML1987]

"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

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Newton**

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@@theshoulderofgiants Leibniz***

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I integrate 1500 times in my Phd Maths Thesis !

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Damn it, why couldn't the video be 2 seconds longer.

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You mean one second?

[@gwaites6329]

hha yea either 2 seconds longer or 1 sec shorter, or even 5 seconds longer so we get 3+33=36

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X D go to about 1:15:42 and put at .5x speed X D sounds like a high californian surfer

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1:15:39 *

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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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Awesome section. I can honestly say, I would have struggled with Calc 2 and 3 without these videos. Years later still helping students.

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you are the best calculus teacher ever!!!!Thank you prof. Leonard

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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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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!!

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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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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

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i am glad that i can follow him through his lecture with less hiccups. Hope he releases videos on diff eq, the troubling partial deq and calc if variations..

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[@tauceti8341]

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

[@liantiu8185]

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

[@georgesadler7830]

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.

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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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integral is mass only if function is mass density 1st: define 3D region between 2 surfaces just like how you can switch between x & y while choosing the outer variable, you can do so with x,y&z here. there are 6 possible ways the bounds of the innermost variable will be functions of the other two variables. the second variable's bounds will be functions of the outermost/independent variable 1:03:21

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you are really good!!! way more good than my professor!! loved your teaching style... lots of love & keep it up!!

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this video really helps me a lot in understanding what triple integrals represent and mean, thanks a lot !!! ❤

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Awesome course, that's now 12 years i'm off the university and with your explanations, everything came back in. In only 3 hours! That's so cool. You're the coolest math prof. i never had......in fact, there were all super-boring without any exception. Two thumbs up!

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Give you credit sir ... You explained what many professors doesn't do ... They just teach for exams not for beneficial use and right applications

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Why do you have to go back through it again?

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I’ve been scrolling KZbin for so long I ended up here. May god bless my soul.

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Love your videos so much! You have saved my Calc 3 grade, I stopped going to class because my professor was so bad and started watching you. Before I got your help I was getting 50% on the quizzes, I’m an all A student so I was terrified, now I’m top in the class with 100% on all my tests.

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Thank you for your time in teaching me .

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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

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I wish my calc professor explained like this and was good looking as well. I would never miss class ever lol

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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.

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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.....

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Prof Leonard is literally helping me ace my calc courses, am actually learning to love math. Wish all of u the same and thanks Prof Leonard

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professor Leonard is our Math Superman.... awesome!

[@charlesfkessler]

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.

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video 33:33 long (almost 33 secs), 333K subscribers, 3 integrals, 3D regions, Calculus 3, I'm scared!

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i spent the day studing this video, easy to understand. Thanks professor Leonard, obrigado!

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You're amazing professor Leonard! Thank you so much!!!

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Bro first video and with In The first five minutes I can tell I wish I had you as my math teacher. So helpful.

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.....and also THANK YOU FOR NOT SKIPPING STEPS!!!! You rock, bruh!!

[@Festus2022]

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.

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Man! This guy is great at what he does. Makes me wish I could go back to school.

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It's all about identifying what's bounded and what's simple. Good video.

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You are Mr. master mind sir......Luv the way u explaining concept.

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Thanks a lot, you are a very good teacher

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I wish there was a professor like you for linear algebra as well

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He will start Linear Algebra in the near future; he said that in his most recent video on this channel.

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+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!

[@ILikeWeatherGuy]

professor leonard is a 4d function of mass density of education. my brain gets smarter as this video goes on.

[@ILikeWeatherGuy]

i.e the mass density of the correct electrons in place in my neurons get denser :D

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I LOVE EVERYTHING ABOUT THIS!! Thank youuu!!!!!

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Such an amazing instructor. Thanks

[@CarlosTorres290]

professor Leonard why did you skip 14.5 ?? also if you have any practice test up to practice !! also thank you for your cal 1 and 2 videos !!! you are my math hero !

[@percycebo50]

What a coincidence cause I'm also writing it on this week. 13.9-14.8

[@ProfessorLeonard]

Not to fear.... Surface Area is covered more generally, and more clearly, in a later section.

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Professor Leonard professor is there any practice questions pdf sets or some book you'd recommend for practice?

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give this man a raise

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You are possibly best Cal 3 Prof!!!

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He wasn't lying about Gary Leonard. That is awesome.

[@John-iy1xi]

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.

[@Peter_1986]

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.

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Happy birthday Leo :D Thanks a lot lot for this videos

[@mariambobat]

Thank you. Thank you. Thank you. I am yet to see your teaching style matched. Much appreciated from Zambia.

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"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

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Hahaha, love to have fun!! But yes, Gary Leonard really is my uncle

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I drank water right before he shouted "'CAUSE I LOVE IT" and almost spat on the screen lmaoo

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Oh😅

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You have a dirty mind LOL

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This was amazingly helpful. Thank you!

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Bad circles, good teaching. I choose you Professor Leonard

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Helped me understand Electrostatics! Thank You Prof Leonard!

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Leonard Deserves an award for being the best professor ever

[@missjdiva]

I'm not even taking calc 3, but I wonder if he does house calls for tutoring? Ow ow! (joking). But seriously, he definitely helped me through retaking Calc 3 as a refresher after 15 years of not having any calc classes. Definitely a great professor!

[@schniependonk]

Once a Professor told us that it is impossible to imagine a more than 3 dimensional space. I was a bit surprised about such a sentence, since you only have to think a little out of the box. Space is nothing more than the playground created by dimensions. A dimension is just an attribute of what the playground describes. So I presented him a 2D picture which shows a 10+D space. It shows a lot of gummibears in all kind of colors, sizes, positions etc. A high dimensional space is immaginable as the playground of all thinkable gummibears in a 3D space. 3D for the Position 3D for the XYZ Size 3D for the Color (Red Green Blue) 2D for the Rotation you also can add lots of finite dimensions. Such as: - gummi bear has only one ear yes/no Actually the human genome uses exactly such binary dimensions. Also the chinese characters where each can contain 6×6 radicals (sub characters). So the space that is created by all thinkable human genomes (GACT-combinations) is quite good immaginable (just go to a big supermarket and look around). Also the space that contains all constructable chinese characters by using 214 available radicals that can be combined within a 6x6 matrix.

[@puffer_fish58]

teacher, you are amazing! greetings from rio de janeiro, brasil, federal university of rio de janeiro

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Professor Leonard, what book does your class use? Thank you for this great video also!

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you are great sir you are very fundamental ...love you and thank you

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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 ❤

[@Yashraj89898]

Dear sir as u told take limits of y as between (r2(square) to 4) ..... I can understand properly but if I take the limit of Y As a (r to 2) den it works....... At 1:54:10

[@blazekilla5553]

importance of using a point IN THE REGION when plugging in to find R-3 simple bounds. I tried (2,2) (which was not in the circle) for fun, and it determined that the wrong function was bigger! So look out for that