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Given a function  in three-dimensional Cartesian space, the value of the surface 
integral 
where S is the surface of a sphere of unit radius and is the outward unit normal vector on S, is
  • a)
  • b)
  • c)
    4π / 3
  • d)
    0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Given a functionin three-dimensional Cartesian space, the value of the...
Given : A function  in three dimensional cartesian space.
Surface integral,

where, S is the surface of sphere of unit radius and is the outward unit normal vector on S.


then, surface integral

By divergence theorem,

I = 3V
Volume of sphere,  (with r = 1 )

Hence, the correct option is (A).
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