I've been studying surface integration by myself, but I'm always stuck at the last step. Consider the above question: This is my approach:
Calculation of the curl of the given field. Calculation of unit vector. Dot product of the unit vector and the curl of the field. Then I projected the Hemisphere surface on the $XY$ plane. In the last step, there is a $Z$.
Now, this is where I face trouble. What should I do with $Z$? Since the area element in the $XY$ plane is $$ds=dxdy$$ my limits of the integration will be in $X$ and $Y$. I thought of replacing the $Z$ with 0(zero) because I am working in $XY$ plane. But then my integrand would diverge. My Question and approach are attached.
