# VC4.23

From Example Problems

Here,

=

=

Therefore,given surface integral= --(1)

If the given surface can be written as ,then the normal vector to S is

Let n denote the unit vector,then we have ,by using(2)

Therefore, --(3)

Also, --(4)

With (3) and (4),(1) gives

=

= --(5)

To transform the double integral on RHS of (5) into polar coordinates,we write so that

Again for the circular region r varies from 0 to a and theta varies from 0 to ,then (5) can be written as

=

= = = [on putting ] = = [By using the formula of ]

= =