Problem 1. [20 pts] (a) [10 pts] Let F = [cos (x), e-y, e-2z], C: r = [2t, t2, 3t], calculate the integral SF(r) . dr based on (x, y, z) starting from (0, 0, 0) to (4, 4, 6). (b) [10 pts] Let F = # + x2y, -y3 , C: r = [t2, t" ], (i) calculate these integrals SF(r) . dr based on (x, y) from (0, 0) to (1, 1) in terms of n; (ii) work out the values of the above line integrals by setting n = 0, 1 and + co (iii) based on result from (ii), state whether above line integral is path independence or not. ("yes" or "no" )