# VC5.23

From Example Problems

The equation of circle is and the parametric equations of C are --(1)

We wish to verify Stokes' theorm that is

--(2)

LHS of (2)=

=

= as on circle(1),z=0,dz=0

=

=

=

=

=

= --(3)

Now,

= --(4)

Let R be the plane circular region PQK bounded by C.Let S1 be the surface consisting of surfaces S and R.Then S1 is a closed surface enclosing volume V(say).By Gauss divergence theorm,we have

--(5)

Since S1 consists of the two surfaces,we have

--(6)

From (5)and (6)we have --(7)

RHS of (2)=

=

=

=

=

= --(8)

Hence from (3) and (8),the Stokes'theorm is verified.