Calculus 3 Lecture 14.6: How to Solve TRIPLE INTEGRALS (Along with Center of Mass and Volume)
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- čas přidán 27. 04. 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***
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Turducken…
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
3:15:00 center of mass
3:22:52 Example 9
thx for helping
Thanks
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You mean one second?
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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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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
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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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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
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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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It's all about identifying what's bounded and what's simple. Good video.
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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!
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Professor Leonard:: "We spent 6 hours doing double integrals"... my class: "we spent 75 minutes doing double integrals"
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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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