is correct, where is the region bounded by the sphere.

incorrect!

A normal unit vector to the sphere is .

soSo the double integral is worth . And I'm stuck here because I have 3 variables ( , and ) but a double integral instead of a triple one.

I know I could solve the problem faster using spherical coordinates, but for the sake of my comprehension let's do it via Cartesian coordinates please.

over the surface of the sphere we have also at the end i used the fact that is the surface area of the sphere, which is