Vector Calculus

**PedroMinsk** · June 21st 2011, 04:47 PM

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

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

S: $x^2 + y^2 = R^2$ , bounded the planes by y = 1 and x + y = 4

A.: $6\pi R^2$

**ojones** · June 24th 2011, 11:28 PM

Something's wrong with the equations for the region $S$ .

**HallsofIvy** · June 25th 2011, 05:32 AM

Originally Posted by PedroMinsk

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

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

S: $x^2 + y^2 = R^2$ , bounded the planes by y = 1 and x + y = 4

Since none of your equations involve z, z can be anything and the region is unbounded.
Were the bounds supposed to be z= 1 and x+ z= 4?

If so is the integral over the cylinder and planes or only over the cylinder?

A.: $6\pi R^2$

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