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CAN SOMEONE PLEASE SOLVE THESE QUESTION ATTACHED TO THIS POST... NEED TO CROSS VERIFY THEM

Mathematics
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1 Attachment
u gotta be kidding me
a scary face popped in my face o.O

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Other answers:

anyway which one do you need help on?
I basically need on 1 and 3
Where are you from, please tell.
Why do you need that info
I have my reasons to ask - basically your nick makes me curious
What do you think @Mikael
If you tell what I asked - the method for all your questions is from the same chapter of knowledge
Lets cut the chase shall we . I hail from India
OK the whole bunch of them is solved by Green's - Stock's formula/theorem
that I know
Soo compute the Curls and integrate - in many cases the curl completely zero or very simple ==> so very easy to integrate
All I want to ask and specifically the 3 ques . In this quest the eqn of the function is bot provided only the curl of the function is provided. Now how shall I find the function from its curl
And conversely: sometimes the line integral [which is fundamentally simpler as it is 1 Dimensional!] will "annihilate" some of the components
@Mikael the question has already given the curl of the function and now what I have to do is to verify it using general method but the problem is that I dont have the function. And by the way if you curl and curl of a function you will always get 0
And Curl is given. Now Find the actual function from the curl is the real task
Wait, wait - what is the strange zeta with dot above mean?
It is the unit vector. And it is a unit vecter in the z direction
CAn't be - because near it IS a unit vector i-with-cap
The unit vectors ARE clear i,j,k with caps above them
That has no meaning to with the question it is just the way our prof. writes.
I have got it - this seems very direct exercise of Gauss-Ostrogradsky theorem http://en.wikipedia.org/wiki/Stokes_theorem
this is simply the z coord.
Aand what ques. 3 is asking is to compute the surface integral of Grad(xyz) = yz*i + xz*j + xy*k
Now read the whole wiki http://en.wikipedia.org/wiki/Stokes_theorem Decide what is more applicable here Stokes or Gauss - Ostrogradsky and get your check
Yeah one IMPORTANT THING : comlete your surface from ONE octant to full 8 octants and use the symmetry of both the FUNCTIO xyz and the Ellipsoid ===> then u can use Gauss-Ostrogradsky
Now I have solved the question
Aand if u do a Volume integral - it separates in PRODUCT of three identical integrals
You should post the method of solution here - courtesy (and even self interest... for the future). I imagine also that u heard about medals and such
Thx and post some general outline - in 2-3 simple printed sentences
You seem to be revolve around medal in here
No it is my PERSONAL folly. You know even Newton was a bit after empty honors...
Aand it would be "morally symmetric" to share the method of solution here for all.
So are u a clg student or go to school. Or work as a teacher or something
or smthng
Ya I will do that in 2-3 days as ringht now I am busy with analog elec

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