22. Determine whether or not the vector field is conservative. If it is, find a function $f$ such
that \(\mathbf{F} = \nabla f\).
(a) \(\mathbf{F}(x, y) = (2x \cos y - y \cos x)\mathbf{i} + (-x^2 \sin y - \sin x)\mathbf{j}
(b) \(\mathbf{F}(x, y) = (1 + 2xy + \ln x)\mathbf{i} + x^2 \mathbf{j}
(c) \(\mathbf{F}(x, y) = e^y \mathbf{i} + xe^y \mathbf{j}
