Let S Be the Boundary Surface of a Solid Region $\int _ { S } \left( ( 4 x + \cos z ) \vec { i } + \left( 3 y + \sin x ^ { 2 } \right) \vec { j } - 5 z \vec { k } \right) \cdot d \vec { A }$

Essay

Let S be the boundary surface of a solid region W with outward-pointing normal.Using an appropriate theorem, change the following flux integral into volume integral over W. $\int _ { S } \left( ( 4 x + \cos z ) \vec { i } + \left( 3 y + \sin x ^ { 2 } \right) \vec { j } - 5 z \vec { k } \right) \cdot d \vec { A }$