Module 17 : Surfaces, Surface Area, Surface integrals, Divergence Theorem and applications
Lecture 51 :  Applications of Divergence theorem [Section 51.2]
  Practice Exercise
  Letbe harmonic functions in such that on , the boundary of . Show that on .
(1)

Using divergence theorem compute the integral

 

where is the surface of the unit cube in bounded by the there coordinate planes and the planes and

.
  Answer
   
(2)
 Find the flux of the field
 

,

across the surface consisting of the hemisphere with base

  Answer
 

 
(3)
 Use divergence theorem to verify that the volume of a solid bounced by a closed surface is given by either of
 

the following:

.
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