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Surface integral of a vector field.

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Please see the attached file for the fully formatted problems.

The flow rate of a fluid is described by vector F in units of kg/m^2/s
It is flowing through a membrane whoes surface S is described by:

S = x^2+y^2+z^2=1 z>sqrt(3/4)

The vector field is defined as:

F(r) = [0,0,2-x^2-y^2+z]

Calculate the rate of mass flow in kg/s by evaluating the surface integral of F over S

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The 4 pages solution shows how to translate the data given to a simple integral (including coordinates transformation) and then continues on to show how to solve it.

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