6. Consider the gradient vector field given by V(f) (x, y, z) = (4x23)i + (6x222 + ez)k. (a) Let c(t) = (sin t, cost, 2), t E [0, "]. Compute V(f) . ds c (b) Let c(t) = (cost, sint, 2), t E [0, 27] be a parametrization of the unit circle, traversed counterclockwise. Calculate V(f) . ds c(c) (Marsden-Tromba 7.2.16) What is the value of the integral of a gradient vector field around a closed curve C? Be sure to justify your answer. 7. (Marsden-Tromba 7.2.14) Let F = (23 + 2xy)i+ (x2)j + (3xz2)k. Show that the integral of F around the circumference of the unit square with vertices (11, +1) is zero