# Stocks question(multivariable calculus)

1. Aug 13, 2009

### slonopotam

calculate
$$\iint_{M}^{}rot(\vec{F})\vec{dS}$$
where
$$\vec{F}=(y^2z,zx,x^2z^2)$$
M is a part of $z=x^2+y^2$ which is located in $1=x^2+y^2$
and its normal vector points outside

i am used to solve it like this
$$\iint_{M}^{}rot\vec{F}\vec{dS}=\iint_{D}\frac{rot\vec{F}\cdot \vec{N}}{|\vec{N}\cdot\vec{K}|}dxdy$$
$$\vec{N}=(2x,2y,-1)$$
$$\iint_{M}^{}\vec{F}\vec{dS}=\iint_{D}\frac{(-x,2xz^2-y^2,z-yz) \cdot (2x,2y,-1)}{1}dxdy$$
now i convert into polar coordinates

x^2+y^2=r
is this method ok?