Use stokes' theorem to evaluate s curl f · ds. f(x, y, z) = 5y cos(z) i + ex sin(z) j + xey k, s is the hemisphere x2 + y2 + z2 = 4, z ≥ 0, oriented upward. step 1 stokes' theorem tells us that if c is the boundary curve of a surface s, then curl f · ds s = c f · dr since s is the hemisphere x2 + y2 + z2 = 4, z ≥ 0 oriented upward, then the boundary curve c is the circle in the xy-plane, x2 + y2 = 4 correct: your answer is correct. seenkey 4 , z = 0, oriented in the counterclockwise direction when viewed from above. a vector equation of c is r(t) = 2 correct: your answer is correct. seenkey 2 cos(t) i + 2 correct: your answer is correct. seenkey 2 sin(t) j + 0k with 0 ≤ t ≤ 2π.