Evaluate the Flux Integral , Where S Is the Surface of the Cylinder X²

Essay

Evaluate the flux integral $\int _ { S } \left( 6 x ^ { 3 } \vec { i } + \left( 6 y ^ { 3 } + \cos z \right) \vec { j } + \left( 7 z ^ { 3 } + 6 y ^ { 2 } + 42 x ^ { 3 } \right) \vec { k } \right) \cdot \vec { d A }$ , where S is the surface of the cylinder x² + y² = 1 bounded by the planes z = -1, z = 1 (including the ends of the cylinder).