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## Homework Statement

verify that the divergence theorem in 3-d is true for the vector field F(r)=<3x,xy,2xz>

on the cube bounded by the planes x=0 x=1 y=0 y=1 z=0 z=1

## Homework Equations

## The Attempt at a Solution

so fristly div(F)=d/dx(3x)+d/dy(xy)+d/dz(2xz)=3+3x

[tex]\int[/tex][tex]\int[/tex][tex]\int[/tex] 3+3xdxdydz=4.5

now i need to evaluate flux through each faces of the cube seperately so i was just wondering if i am doing this write say i would want to evaluate the top surface of the cube

then i would have to parametrize it so would the following be corret

r(x,y,z)=(3x,xy,1)

dr/dx=(3,y,0)

dr/dy=(0,x,0)

(dr/dx) X (dr/dy) = (0,0,3x)

r(x,y,z).((dr/dx) X(dr/dy))= (3x,xy,1).(0,0,3x) = 3x

[tex]\int[/tex][tex]\int[/tex] 3x dydx

=3/2

and i have to do the same for all other five surfaces so is this the correct way?