6. Let F(x, y, z) = (x3 +sin(zy), y3 +arctan(xz*2),3z) and S be the closed surface (oriented with outward pointing normal) consisting of the circular cone z = 1 - vx2 + yz closed below by the plane z = 0. Evaluate the surface integral F . ds. S Ans: 13 10 .TT 7. Consider the vector field F(x, y, z) = ( sin(eyz), cos(eTZ), ex2 tez ? ). (a) Find curl F. (b) Find the flux of G := curl F across S, where S is the part of the paraboloid z = 9 - x2 - y?, with z > 0 oriented with a downward pointing normal. Ans: (a) VXF = (2yey + xetz sin(etz), yeyz cos(eyz) - 2xet , -zetz sin(etz) - zeyz cos(eyz ) Ans: (b) 0