# Divergence theorem problem

1. Dec 6, 2014

### s3a

1. The problem statement, all variables and given/known data
Find the outward flux of the radial vector field F(x,y,z) = x i^ + y j^ + z k^ through the boundary of domain in R^3 given by two inequalities x^2 + y^2 + z^2 ≤ 2 and z ≥ x^2 + y^2.

2. Relevant equations
Divergence theorem: ∫∫_S Fn^ = ∫∫∫_D div F dV

3. The attempt at a solution
Is the final answer correct in TheSolution.jpg (because I get 2*pi/3 * (2^(3/2) - 1) - pi/2)?

If someone could check if I'm right or wrong, I would REALLY appreciate it!

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2. Dec 6, 2014

### s3a

Actually, I get π * [2(2^[3/2] - 1) - 3/2] (where my answer's 2^[3/2] differs with the √(2) in the attachment).

Last edited: Dec 6, 2014
3. Dec 6, 2014

### Zondrina

There appears to be a typo near the front of the answer. That $2$ should not be in front of the divergence integral.

4. Dec 6, 2014

### s3a

Thanks for pointing that out.

Are the parts where the author begins to use the letter "t" and, most importantly, the final answer correct?

5. Dec 7, 2014

6. Dec 7, 2014

### s3a

Actually, my answer (from the second post in this thread) is the same as three times yours, so it appears that I was correct and that the solution was incorrect.

I'm posting my latest work, just in case I'm right by fluke (so please confirm).

File size:
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File size:
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7. Dec 7, 2014

### Zondrina

Sorry about that. I forgot the 3 so the answer should be 6.78.

8. Dec 7, 2014

### s3a

That's the same thing I got (and not what the solution that I attached in my first post in this thread got).

It must not have seemed like a lot to you, but your confirmation was very helpful to me, so thanks for helping me confirm! :)

9. Dec 7, 2014

### Zondrina

Wolfram is good for self error checking, but matlab's dblquad and triplequad functions are also a very good option.

10. Dec 7, 2014

### s3a

Thanks as well for mentioning those, but I meant having another human being to confirm was useful, because I'm stressed and exhausted and studying for exams, so I wanted to make sure I wasn't making a mistake in the setup of the computation (because one makes more mistakes when stressed and/or exhausted).