F is the three-dimensional vector field defined by F(x,y,z) = (x,y,z). In other terms, P(x,y,z) = x, Q(x,y,z) = y, R( x,y,z) = z. Also, the domain D = [0,1]x[0,1]x[0,1] is the solid unit cube, which...


F is the three-dimensional vector field defined by F(x,y,z) = (x,y,z). In other terms,


P(x,y,z) = x, Q(x,y,z) = y, R( x,y,z) = z.


Also, the domain D = [0,1]x[0,1]x[0,1] is the solid unit cube, which consists of every (x,y,z) such that


0 <= x=""><= 1="" and="" 0=""><= y=""><= 1="" and=""><= z=""><=>


The surface S of the cube D consists of six square faces, with normals pointing out of the cube.



Question: Calculate the flux of F across the surface S of the cube D.



Jun 05, 2022
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