Stoke Theorem

Stoke Theorem:

Statement: If S is a surface bounded by a simple closed curve C and if is any continuously differentiable vector function then,

Example 1. Verify Stoke theorem for the vector taken round the rectangle bounded by x = 0, x = a, y = 0, y = b.

Solution: By Stoke Theorem:

For the surface, 

Hence.                                                                  LHS = RHS