Module 17 : Surfaces, Surface Area, Surface integrals, Divergence Theorem and applications
Lecture 50 : Application of surface integrals [Section 50.2]
 

Thus, for

and this is the outward normal for the upper hemisphere as the component is positive. Similarly, the surface , has parameterization

and

But, this is not the outward normal, as the component is positive. In fact, the outward normal for is given by

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