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is the solid sphere with radius 2 centered at the origin. However, since the problem says it's only the upper hemisphere, therefore, . Therefore, the answer is:
Note that the region is only the upper hemisphere of a sphere centered at the origin and with radius 2. Since z-axis is the vertical axis, this means that the sphere only consists of points with .
Thus, by following the equation of a sphere centered at the origin, we have:
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