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Let's say I have

$\int \int _{S((x_0, y_0, z_0), r)}$

In other words, the sphere of radius $r$ centered at the point $(x_0, y_0, z_0)$

First of all, I'm not sure if the notation is referring to a surface integral or a volume integral. There are two integral signs, so I'm leaning more towards surface.

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    So what is your question? Either a) interpretation of the notation, or b) how to work out the specific integral you stated ? – 2017-01-26
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    My main question is: given the notation, is it a surface integral? I think it is, because if it wasn't a surface integral, we would have three integral signs? – 2017-01-26
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    I think I can rewrite the integral if it is not a surface integral. I would change it into spherical and have something like this: $\int_0^{2\pi} \int _{-\pi/2}^{\pi/2} \int _0^r$. – 2017-01-26

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