Compute $$\int \int _S F \cdot n \hspace{2mm} dS$$ where $S$ is the surface of the cube bounded by the six planes $$x=0,\hspace{2mm}x=2,\hspace{2mm}y=0,\hspace{2mm}y=4,\hspace{2mm}z=0, \hspace{2mm} z=1$$ $n$ is the outward normal and $$F(x,y,z)=\bigg(y^2-\sin(yz), \frac{\cos(x)}{x^2}-y-z, x^2y+x^2+y^2\bigg)$$
First, this is a cuboid isn't it? Its not a cube, not all the edges are of equal length...
It seems like $div (F)=-1$ so correct me if I am wrong but we can do $$-\int \int \int _V dxdydz$$ which equals the volume of the cuboid right? So the answer is -8?
I feel like I am doing something wrong...