Definujme plo�n� integr�l 2. druhu pomoc� vzore�ku
$$
\int \! \BBb F {d \vec S} :=
\int _{D} \! \Bbb F (S(u,v)) \cdot n(u,v)
{du dv} \quad ,
$$
kde $S : D \to R^3$,
$S(u,v) = (x(u,v),y(u,v),z(u,v))$ je parametrizace plochy a 
$n(u,v)$ je norm�lov� vektor k plo�e 
$S$ v bod� $S(u,v)$ definovan� jako vektorov� sou�in 
$$
n(u,v) := ({\frac {\partial x}{\partial u}},
{\frac {\partial y}{\partial u}},{\frac {\partial z}
{\partial u}}
) \times ({\frac {\partial x}{\partial v}},
{\frac {\partial y}{\partial v}},
{\frac {\partial z}{\partial v}}) \quad .
$$


Spo�t�te, �e $\int \! \BBb F {d \vec S} = 0$ pro 
$\Bbb F(x,y,z) = (0,0,1)$ a $S(u,v) = (u,v,0)$,
$D= \{(u,v) \in \Bbb R ^2$, $u^2 + v ^2 \le 1
\} $. 
