been trying to solve the folowing area calc:

$\displaystyle

S=\{(x,y,z) | x^2 + z^2 = 1, y^2+z^2\leq 1. z\geq 0\}

$

so it should be the area of the surface $\displaystyle z=\sqrt{1-x^2}-\sqrt{1-y^2}$

then to use the formula for area integrals over uneven surfaces

$\displaystyle \int \int \sqrt{ (\frac{df}{dx})^2 + (\frac {df}{dy})^2 + 1} $

i derive as follows:

$\displaystyle

\frac{dz}{dx} = \frac{-x}{ \sqrt{1-x^2}}

$

$\displaystyle

\frac{dz}{dy} = \frac {y}{\sqrt{1-y^2}}

$

and then in to the formula:

$\displaystyle \int \int \sqrt{ (\frac{-x}{ \sqrt(1-x^2)})^2 + (\frac {y}{\sqrt(1-y^2)})^2 + 1}dxdy $

but then i'm stucked, anyone got an idea how to solve this one?