Consider the field F(x,y,z)=(yz,xz,xy) and the region \Omega defined for x\ge0,\,y\ge0,0\le z\le b and 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 x=0,y=0,z=0,z=b and x^2+y^2=a^2 to compute the flux integrals?

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

I really need help on this one.