Step 1:

Work done by force in moving a particle along the path is .

Stokes theorem:

.

Step 2:

The function is .

If then .

.

Step 3:

Find the plane equation, for points and .

Let the equation of the plane is .

The point on the plane is

.

The point on the plane is .

The point on the plane is

Substitute , in .

Substitute   in above expression.

The plane equation is .

Step 4:

.

Where , is the projection of the surface on the plane and is the plane equation.

.

.

Substitute in above expression.

.

Step 5:

is the projection of the surface on the plane.

is the region inside the points and .

From the points and .

.

.

The work done is .

Solution:

The work done is .