Use the Divergence Theorem to calculate the surface integral ffs F - dS where F(x,y, z)=xyzi+xyzj+xyzk and S is the surface of the box enclosed by the planes x=-2, x = 6, y =-1 y = 4, z = 0 and z =9 O 1,688 O 10,125 O 6,750 O-3,375 O 5,063

Find the area of the surface given by z = f(x, y) that lies above the region R f(x, y) = 19 + 7x-3y R: square with vertices (0, 0), (6, 0), (0, 6), (6, 6)

Suppose F = (y + 2x, 7x + 4z, 6y + 2x) and S is a surface bounded by C, a circle with radius 3, center at (2, 0, 0), in the plane x = 2, and oriented counterclockwise as viewed from the origin (0, 0, 0). Find the flux of curl(F) across S and then evaluate the circulation & F. dr. (Use symbolic notation and fractions where needed.) DS Incorrect JC curl(F). dS = F. dr = 18T Incorrect 18A

a surface is defined by the parametric form. S(u,v)= X(u,v)i + Y(u,v)j + Z(u,v)k, where 0<= u <=2pi and 0<= v <=1 X(u,v) = (v2+1)cos2u Y(u,v) =vsinu Z(u,v) =-(v2+1) a. determine the normal vector of the surface S b. determine the unit normal vector of S(0,1/2) that point onward