Calculate the line integral of the function v = x2x + 2yz y + y2 z 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, l);

(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)?