(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

First a thanks for the existence of this site, i find it quite useful but had no need to actually post till now.

I am stuck on the following problem in "introduction to physics"

We should calculate the [itex]\oint[/itex] [itex]\vec{v}[/itex].d[itex]\vec{A}[/itex]

of a object with the following parameters Vol = x^2+y+2<4, 0<z<4-x^2-y^2

with [itex]\vec{v}[/itex] being x+y,y+z,x+z)

with and without the div. theorem,

2. Relevant equations

Divergence theorem,div = 3 - simple cylinder integral = possible solution =32pi

Parametrization of volume as

2cos(u)sin(v)

2sin(u)sin(v)

4cos(v)

u = (0,2pi) v= (0,pi/2)

Surface integration using [itex]\vec{v}[/itex](u,v).ru x rv

3. The attempt at a solution

I have 32Pi as a solution using the div theorem,

and i am in over 2 pages of writing now without using it,

Am i missing something or is this the kind of problem that only exist "to show you how useful something is" and i really should come to some horrible solution that is taking a double integral of something over 50 symbols long ?

Thanks in advance.

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# Surface integral of a vector field w/o div. theorem

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