Calculus 3 Lecture 14.6: How to Solve TRIPLE INTEGRALS (Along with Center of Mass and Volume)
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- Опубліковано 27 кві 2016
- 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)
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.
"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
Newton**
@@theshoulderofgiants Leibniz***
dis sound like a yaad man mek dis comment.
Turducken…
I integrate 1500 times in my Phd Maths Thesis !
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.
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
3:15:00 center of mass
3:22:52 Example 9
thx for helping
Thanks
Damn it, why couldn't the video be 2 seconds longer.
You mean one second?
hha yea either 2 seconds longer or 1 sec shorter, or even 5 seconds longer so we get 3+33=36
X D go to about 1:15:42 and put at .5x speed X D sounds like a high californian surfer
1:15:39 *
G Waites lmfao
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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.
It is also following closely the "Calculus" 10th edition by Ron Larson and Bruce Edwards
Early Transcendentals 8th edition too
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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
It's all about identifying what's bounded and what's simple. Good video.
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ابداااااع ...
ليت بعض الدكاتتره يتعلموا منك ..
this video really helps me a lot in understanding what triple integrals represent and mean, thanks a lot !!! ❤
.....and also THANK YOU FOR NOT SKIPPING STEPS!!!! You rock, bruh!!
crushing my calculus tests easily after watching this far.
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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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
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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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.
When talking about First Moments, what does it mean to have a 3D object rotating about a plane?
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Professor Leonard how would do the example at about 1:24:45 if z were from 0 to 2x^2 , because when solving for the intercepts each of the three solutions are in z's domain
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Estou gostando muito dos seus vídeos, dando like em todos.
What a great lecture