first of all z = x^2 +y^2 is a parabaloid
secondly 0 < x < 1 and 0 < y < 1
is a square not a circle so you want to stay with rectangular coordinates
with limits 0 to 1 for both x and y
calculate
where
M is a part of hyperboloid
which is located at 0<=x<=1 and 0<=y<=1 ,and its normal vector points outside
like this :
http://i28.tinypic.com/f9p63r.gif
i am used to solve it like this
now i convert into polar coordinates
x^2+y^2=r
how to what are the intervals for r
i just guessed its from 0 to 1
i dont know how to know the upper interval here
except that
is this method ok?