Vector Calculus (area)

**PedroMinsk** · June 21st 2011, 04:36 AM

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.: $-40pi$

**FernandoRevilla** · June 21st 2011, 06:48 AM

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 $S_2:x^2+y^2=1,\;0\leq z \leq 1$ .

**PedroMinsk** · June 21st 2011, 05:26 PM

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

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