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

While evaluating, care must be taken the integrals on right hand side since is oriented. Suppose, we select the positive orientation for the normal. Then for

,

(iv) If and are expressed in terms of their components:

then

and hence

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