# Math Help - Vector Calculus (area)

1. ## Vector Calculus (area)

Calculate $\iint\limits_S \vec{F} .\vec{n} dS$:

$\vec{F}(x,y,z)$ = (x,y 2x - x - y)

S: $x^{2} + y^{2} - z^{2} = 0$, $\ 1 \leq z \leq 4$ and $x^2 + y^2 = 1$, $\ 0 \leq z \leq 1$

Answer.: $-40pi$

2. ## Re: Vector Calculus (area)

Hint: Decompose the integral as $\iint_{S_1}F\cdot n\;dS+\iint_{S_2}F\cdot n\;dS$ with $S_1:x^2+y^2-z^2=0,\;1\leq z \leq 4$ and $S_2:x^2+y^2=1,\;0\leq z \leq 1$ .

3. ## Re: Vector Calculus (area)

Thanks very much. I'll try to solve it in this way.