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 0<= z <= 1. 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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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 0<= z <= 1.

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.

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