Originally Posted by

**headaches11**

$\displaystyle \mathop\int\int\limits_{\hspace{-15pt}\text{Red}} \sqrt{f_x^2+f_y^2+1}dxdy$

I do not understand where the above expression has come from? (is it a well known formula?) and why have you used f(x,y) and not f(x,y,z) as we are in 3d.

does z= f(x,y)?

i.e $\displaystyle z^2 = a^2 - ( x^2 +y^2)$

therefore $\displaystyle z = sqrt(a^2 - ( x^2 +y^2)) $... is this where your f(x,y) came from?

And what does the notation $\displaystyle f_x^2 $ mean? (im assuming a derivative wrt x?)