Check Divergence Theorem on Unit Cube

[Saladsamurai]

Homework Statement

Check the Divergence Theorem \int_V(\nabla\cdot\bold{v})\,d\tau=\oint_S\bold{v}\cdot d\bold{a}

using the function \bold{v}=<y^2, 2xy+z^2, 2yz> and the unit cube below.

Now when I calculate the divergence I get
(\nabla\cdot\bold{v})=2y+2x+2y

but Griffith's says that it is 2(x+y)

before I continue, I need to know what the heck I am missing?

 

[Defennder]

Now when I calculate the divergence I get
(\nabla\cdot\bold{v})=2y+2x+2y

How did you get that? You should have \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z}. Check your first term \frac{\partial v_x}{\partial x}.

 

[Saladsamurai]

How did you get that? You should have \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z}. Check your first term \frac{\partial v_x}{\partial x}.

Oh man. Thanks Defennder. I am a retard