Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F = 2i +2j + 2k across the surface S.

Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the paraboloid z = 3 - x² - y² in above the plane z = -1 with upward orientation.

Compute the flux of the vector field = zi + 4y3 through the cylindrical surface shown below, if a = 2 and b = 2 and it is oriented away from the z-axis. flux = a

Pls explain in detail thx