Step 1:

The function is .

(a)

Find the potential function .

To find the potential function, follow the condition .

From above, , and .

Integrate with respect to x.

           equation (1)

Differentiate equation (1) with respect to y.

          equation (2)

Compare equation (2) and .

                                        equation (3)

Integrate equation (3) with respect to y.

Substitute in equation (1)

                equation (4)

Differentiate equation (4) with respect to z.

               equation (5)

Compare equation (5) and .

                                          equation (6)

Integrate equation (6) with respect to z.

Substitute in equation (4).

.

Step 2:

(b)

Find .

But , then .

In a smooth curve C, vector function in the interval , whose gradient vector is continuous on C then

.

C is the line segment from .

Then

Solution :

(a) .

(b) .