Use the Divergence Theorem to find the outward flux of F = (12x3 + 15xy?) i+ (7y3 + 5e'sin z) j+ (12z3 + 5e'cos z) k across the boundary of the region D: the solid region between the spheres x~ +y2 + z2 = 1 and x2 + y2 +z2 =2. The outward flux of F = (12x3 + 15xy?) i+ (7y3 + 5esin z) j+ (12z3 + 5e'cos z) k is (Type an exact anwer, using x as needed.)- Let C be the curve (x - 3)" + 4(y - 2)" =36, 3x + 3y + z =1, oriented counterclockwise when viewed from high on the z-axis. Let F be as shown below. Evaluate & F . dr. F = (3z2 + y2 + sinx?) i+ (2xy +z)j + (3xz + 2yz)k OF . dr= (Type an exact answer.)-Find the circulation of F = - yi + 2x-j + 4zk around the oriented boundary of the part of the paraboloid z = 25 - x" - y lying above the xy-plane and having normal field pointing upward. The circulation is (Type an exact answer.)