Verification of Divergence Theorem

[sunnyday11]

Homework Statement

F(x,y,z) = (2x-z) i + x²y j + xz² k and the volume is defined by [0,0,0] and [1,1,1].

Homework Equations

flux integral = $$\int\int\int$$ div F dV

The Attempt at a Solution

$$\int\int\int$$ div F dV = $$\int\int\int$$ (2+x²-2xz)dxdydz

= 2 + 1/3 - 1/2 = 11/12

But I have no idea how to calculate the flux integral because the methods I learned was to use z=f(x,y) with the unit normal vector.

Thank you very much!

 

[ojs]

But I have no idea how to calculate the flux integral because the methods I learned was to use z=f(x,y) with the unit normal vector.

Thank you very much!

Thats sort of what you have to do, you have to divide your volume into pieces, find a normal for each piece (I assume here that this is a cube with one corner in (0,0,0) and one in (1,1,1)) and do the surface integral for each side (so 6 integrals in the whole).

But use the identity $$\oint_S = F \bullet d\textbf{s}$$