Consider the vector field F~ (x, y, z) = −ye−z 2 sin x ˆı + x(1 + y 2 z 2 ) 3/2 ˆ + x 3 + y 2 (1 + z 2 ) 4 kˆ. Let S = x 2 + y 2 + z 2 25 = 1, z ≥ 0 . Compute Z Z S (∇ × F~ ) · ~n dσ.