- #1
hils0005
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Homework Statement
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).
Homework Equations
[tex]\int[/tex][tex]\int[/tex] [tex]\widehat{}F[/tex] [tex]\bullet[/tex] (-partial z/dx i -partial z/dy j + k) dxdy
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?