Evaluate with the help of divergence theorm the integral , where S is the entire surface of the hemispherical region bounded by .
Let V be the volume enclosed by S.Hence S is the point of the sphere given.
By divergence theorem,
To simplify the triple integral,we use the spherical polar coordinates so that --(2)
In order to cover the volume,the limits are r=0 to a
Using (3) in (1),we see that the value of the given surface integral is