# Math Help - Vector Calculus

1. ## Vector Calculus

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.: $6\pi R^2$

2. ## Re: Vector Calculus

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

3. ## Re: Vector Calculus

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.: $6\pi R^2$