Originally Posted by

**transgalactic** calculate

$\displaystyle

\iint_{M}^{}rot(\vec{F})\vec{dS}

$

where

$\displaystyle

\vec{F}=(y^2z,zx,x^2z^2)

$

M is a part of $\displaystyle z=x^2+y^2$ which is located in $\displaystyle 1=x^2+y^2$

and its normal vector points outside

i am used to solve it like this

$\displaystyle

\iint_{M}^{}rot\vec{F}\vec{dS}=\iint_{D}\frac{rot\ vec{F}\cdot \vec{N}}{|\vec{N}\cdot\vec{K}|}dxdy

$

$\displaystyle

\vec{N}=(2x,2y,-1)

$

$\displaystyle

\iint_{M}^{}\vec{F}\vec{dS}=\iint_{D}\frac{(-x,2xz^2-y^2,z-yz) \cdot (2x,2y,-1)}{1}dxdy

$

now i convert into polar coordinates

x^2+y^2=r

is this method ok?