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, which in my case will give

, which will give just

Dunno if it is correct
Also found another approach but there I got quite unpleasant integral.

This surface is the graph of the function

, so use the graph parametrization

We shall use the following (very important!) general formula for the upward normal of a surface defined by an equation of the form

   

For the surface of interest here, it follows that:

And we have

So

So we have