4. (10 pts) (a) Describe the Stoke's Theorem. (b) Let F = y cos (xz) i + xeyz } - xyz k, and let S be the part ofnthe pshere x + y + (z 2) 2 = 8 that lies above xy-plane with outward normal vector . Evaluate ] F. ds. Hint: You need to use the Stoke's Theorem and the Green's Theorem. Consider the domain D on the xy-plane enclosed the by the boundary C of the S. Regarding the surface S and its boundary C, you need the Stoke's theorem. then, regarding the domain D and its boundary C, you need to use Green's Theorem. then the walking direction. Stoke's Theorem Let S be an oriented surface that is bounded by a simple closed boundary curve C with positive orientation. If F: IR-> IR is a Vector field, then C dz = SS arl (F) ds S The compatibility of the orientation of 5 and its boundary C is very important.