(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the total flux of vectorF(x,y,z)=8x^2y i + 6yz^2 j + y^3z k outward through the cube whose verticies are(0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1),(1,1,1), (0,1,1).

2. Relevant equations

[tex]\int[/tex][tex]\int[/tex] [tex]\widehat{}F[/tex] [tex]\bullet[/tex] (-partial z/dx i -partial z/dy j + k) dxdy

3. The attempt at a solution

I set up the surface S: xyz[tex]\leq[/tex] 1

so z [tex]\leq[/tex] 1/xy

dz/dx= 1/y lnx

dz/dy= 1/x lny

so F (dot) (-dz/dz i -dz/dy j + k)

=-8x^2lnx - (6yz^2lny)/x + y^3z

I then plugged in z

=-8x^2lnx - 6lny/x^3y + y^2/x

[tex]\int[/tex][tex]\int[/tex] =-8x^2lnx - 6lny/x^3y + y^2/x dxdy

0 [tex]\leq[/tex] x [tex]\leq[/tex] 1

0 [tex]\leq[/tex] y [tex]\leq[/tex] 1

Does this look correct?

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# Homework Help: Total Flux through a cube

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