Calculate the line integral of the function from the origin to the point (1,1,1) by thre...

Calculate the line integral of the function from the origin to the point (1,1,1) by three different routes:

(a) (0, 0, 0) → (1, 0, 0) → (1, 1, 0) → (1, 1, 1).

(b) (0, 0, 0) → (0, 0, 1) → (0, 1, 1) → (1, 1, 1).

(c) The direct straight line.

(d) What is the line integral around the closed loop that goes out along path (a) and back along path (b)?