Use stokes' theorem to evaluate s curl f · ds. f(x, y, z) = zeyi + x cos(y)j + xz sin(y)k, s is the hemisphere x2 + y2 + z2 = 4, y ≥ 0, oriented in the direction of the positive y-axis.

Jake volunteers to out his younger brother's basketball team in his free time. one of his tasks is to ensure that all the basketballs have enough air in them. given that a properly inflated basketball measures 8.8 inches across, what is the total volume of air inside six of jake’s basketballs? assume that the wall of each ball is infinitely thin.