Consider the field $\displaystyle F(x,y,z)=(yz,xz,xy)$ and the region $\displaystyle \Omega$ defined for $\displaystyle x\ge0,\,y\ge0,0\le z\le b$ and $\displaystyle x^2+y^2=a^2,\,a,b>0.$

I need to evaluate the flux integrals of the field over each one of the five faces of the region. Consider the exterior orientation.

I'm a bit lost here, do I have to consider $\displaystyle x=0,y=0,z=0,z=b$ and $\displaystyle x^2+y^2=a^2$ to compute the flux integrals?

For example for $\displaystyle x=0,$ how is it done?

I really need help on this one.