Problem 22. Show that the given vector field is conservative and use the fundamental theorem to calculate the line integral $\int_C \mathbf{F} \cdot d\mathbf{R}$ along a piece-wise smooth curve joining A(10, -1), B(0, -1, 1).
a. $\mathbf{F}(x, y, z) = (\sin z, -z \sin yx \cos z + \cos y)$
b. $\mathbf{F}(x, y, z) = (3x^2y^2z, 2x^3yz, x^3y^2 - e^{-z})$