# VC5.50

From Example Problems

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,

=

= --(1)

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

Here

=

=

=

=

=

= --(3)

Using (3) in (1),we see that the value of the given surface integral is