# calculating flux through a surface

• Apr 21st 2009, 12:20 PM
TheRekz
calculating flux through a surface
My question is:

Compute the flux of the vector field, $\vec{F}$ , through the surface, S.
$\vec{F} = 7\vec{r}$ and S is the part of the surface $z = x^2 + y^2$ above the disk $x^2 + y^2 \leq 4$ oriented downward.

$\int\limits_R (7x\vec{i} + 7y\vec{j} + (x^2 + y^2)\vec{k}) \cdot (2x\vec{i} + 2y\vec{j} - k) dA$
$\int\limits_R (14x^2 + 14y^2 - (x^2 + y^2)) dA$
$\int\limits_R (13x^2 + 13y^2) dA$
$13 \int\limits_R (x^2 + y^2) dA$
$13 \int^{2\pi}_0\int^2_0 r^3 dr d\theta$
$13 \int^{2\pi}_0 4 d\theta$

$104\pi$

is this correct?
• Apr 21st 2009, 02:28 PM
Calculus26
yes but for one cosmetic change

in you next to last integral you should have replaced dA with drdtheta since dA is rdrdtheta

--in your last integral dA should be dtheta
• Apr 21st 2009, 02:30 PM
TheRekz
ok my bad , edited my original post, however my final result that I got is:

$1664\pi$, and this is a web assign question and it doesn't accepts it (marks it as wrong)
• Apr 21st 2009, 02:34 PM
Calculus26
Aah-- I didn't see it either r varies from 0 to 2 not 4

The radius of the disk is 2
• Apr 21st 2009, 02:36 PM
TheRekz
I tried $104\pi$ and it doesn't work as well
• Apr 21st 2009, 02:38 PM
Calculus26
In your first integral you have 7x +7y +z --should be 7x+7y+7z
• Apr 21st 2009, 02:41 PM
TheRekz
thanks I got it now :)