Module 17 : Surfaces, Surface Area, Surface integrals, Divergence Theorem and applications
Lecture 51 :  Divergence theorem [Section 51.1]
51.1.1 Theorem (Divergence theorem):
  Proo f(For Simple regions ):
 


                Figure 222. Caption text.


Note that on the surface the and that the outward normal makes with is acute, on it is obtuse and on it is . Hence, above becomes

This proves . Similarly, using the special nature of and projecting it on -plane and -plane, respectively, equations and can be proved. This proves the divergence theorem for special regions.

 
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