2. a) Let C be curve obtained by intersecting of the cylinder a ty? = 1 with the plane r = z, oriented counterclockwise if looking from the positive direction of the z-axis. Verify the Stoke's theorem, by calculating /(z + y)do + rydz directly, C as well as by transitioning to a surface integral. 5 b) Evaluate (y + sinx) der + (22 + cosy)dy + i'dz, C where C is parameterized by r(t) = (sint, cost, sin 2t), te [0, 2x]. Hint: C lies on the surface z = 2ry. 5