The Green's Theorem may be used to calculate the line integral (work) done by moving an object inpath C that is the boundary of a closed region R. The Green's Theorem is written as follows:

Where M and N are the x and y components of the force F and dA is dydx.

This line integral is the equivalent of the work done when the object moves from the starting point in a counterclockwise movement back to the original point.

Procedure - determine the value of the line integral for the closed region which is defined by the two curves y = x and y = x2. The force acting on the object is the vector . The points of intersection of the two curves are 0,0 and 1,1

SOLVE the following using Green's Theorem