Consider the three-dimensional vector field F(x, y, z) = (x xz,x - yz, z2). Let...

Transcribed Image Text:

Consider the three-dimensional vector field F(x, y, z) = (x – xz,x - yz, z2). Let S be the part of the paraboloid z = 1- x2 – y? that lies above the xy-plane, oriented upward. Let C be the oriented curve given by the parametrisation c(t) = (cos t, sin t, 0) for 0 st< 27. Directly evaluate the surface integral | c url F· dS. (a) Directly evaluate the line integral F (b) Consider the three-dimensional vector field F(x, y, z) = (x – xz,x - yz, z2). Let S be the part of the paraboloid z = 1- x2 – y? that lies above the xy-plane, oriented upward. Let C be the oriented curve given by the parametrisation c(t) = (cos t, sin t, 0) for 0 st< 27. Directly evaluate the surface integral | c url F· dS. (a) Directly evaluate the line integral F (b)