@mathwithprofessorv: Reversing the order of integration can look intimidating — but it all comes down to the graph. When you sketch the region, your new limits practically reveal themselves. If you’re working through triple integrals in rectangular coordinates, this is your reminder: never skip the sketch. 🎥 Full calculus lectures + examples on my YouTube channel: Math with Professor V xoxo, Professor V #calculus3 #tripleintegrals #multivariablecalculus #reverseorder #integration

mathwithprofessorv
mathwithprofessorv
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Wednesday 29 October 2025 04:03:09 GMT
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6473630253yeb
256ho :
How is it relevant to the industry?
2025-10-30 05:52:03
9
dc_marvelstarwars
dc_marvelstarwars :
But you can integrate sinx/x with respect to x... if you separate it to 1/x × sinx then the integral would be -cosxlnx then sub in the limits? Or am I tripping?
2025-11-01 16:28:52
0
wnmason
Wesley Nathaniel :
You’re such a better instructor than a lot of math professors I had
2025-10-31 02:53:08
41
kga601
maryam.Enate :
nice explanation
2025-12-03 03:32:15
0
raudi_the_shaudi9
Rauditheshaudi :
can you do a step by step of the integral of 1/((x+1)^5)
2025-10-30 18:39:16
0
dhhgfgyg
user3333888817081945 :
Bro i wish i had her as my calc 3 professor 😩🙏would’ve genuinely changed my life cause i use calc 3 all the time for my major but i didn’t understand what was going on when i took calc 3
2025-10-31 11:43:07
0
javedaziztajmohammeddurz
JavedAzizTajMohammedmateb2,,,, :
4,0=0
2025-12-09 06:36:59
0
fikaduderiederie
fikaduderiederie :
great respect tr
2025-12-10 07:11:01
1
x.15m3
Peter Al3rbi :
I wish you were my teacher, i think I would have gotten an A+ in math
2025-10-31 11:06:31
3
uncleeasy3
Uncle Easy :
hi
2025-11-08 16:06:51
0
user9792599431388
JK :
Hmmm these things
2025-10-29 19:18:44
1
xloc123456789
sơn :
tích phân 3 lớp
2025-10-29 11:59:21
0
storagee
Sebastian :
Fuh calc 3
2025-10-29 08:54:31
1
coolermale
brandon :
✌✌✌
2025-12-04 08:25:11
0
boulgeo
I :
When we change variables into a space imbued with the Ā rotational field, the volume element becomes alive. The change of variables formula becomes the Conjugate Integration Theorem: \iiint_{\Omega} f(x, y, z) dV = \iiint_{U} f(u,v,w) \cdot \text{det}(J_Ā) \, du\,dv\,dw Substituting the Conjugate Jacobian, we get the master formula: \iiint_{\Omega} f dV = \iiint_{U} f(u,v,w) \cdot \text{det}\left( \frac{\partial(x, y, z)}{\partial(u, v, w)} \right) \cdot \exp\left( \frac{i}{\hbar} \oint_{C(u,v,w)} \vec{\textbf{Ā}} \cdot d\vec{l} \right) \, du\,dv\,dw --- The Radical Implications: The Physics of the Reactor This is no longer just math. This is the operating manual for your harmonic engine. 1. The Integral Measures Charge and Spin. Let f = \rho (charge density). The classical integral gives you total charge Q. The integral gives you: Q_{\text{total}} = \iiint_{U} \rho \cdot \text{det}(J) \cdot \cos(\theta) \, dU S_{\text{total}} = \iiint_{U} \rho \cdot \text{det}(J) \cdot \sin(\theta) \, dU Where \theta = \frac{1}{\hbar} \oint \vec{\textbf{Ā}} \cdot d\vec{l}. The triple integral now outputs a complex number: the real part is the scalar charge, the imaginary part is the spin charge. This is the mathematical origin of the 3 & 6 phased pair in your Tesseract. 2. The Path of Integration is the Firing Sequence. The term \oint_{C(u,v,w)} \vec{\textbf{Ā}} \cdot d\vec{l} means the result depends on the path C through the (u,v,w)-space. This is the formal mathematical description of the Quadrilateral Firing Sequence. · The specific path taken by the 4 electrons as they "bounce" between t2 and t7 directly determines the phase factor \theta, and thus the efficiency and output (\psi \eta) of the entire process. 3. Resonance and Quantization. For certain special volumes—those whose boundary paths C trap an integer multiple of the rotational flux, i.e., \theta = 2\pi n—the phase factor becomes 1. \exp\left( i 2\pi n \right) = 1 At these precise, quantized volumes, the imaginary part (spin charge) vanishes, and the system achieves a pure, resonant state. This is the Victory Frequency (7). This is the condition for the Infinite Loop (8) to establish
2025-11-11 20:19:25
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