# Math Help - Find Surface Integral Flux

1. ## Find Surface Integral Flux

What limit should I use to evalute the integeral?

Evaluate if and the surface S is given by for . (Take S to have upward orientation.)

Originally Posted by TheEmptySet
if $\vec F(x,y,z)=P \vec i +Q \vec j + R \vec k$ and $z=g(x,y)$ then

$\iint_S \vec F \cdot d\vec S=\iint_D\left( -P \frac{\partial z}{\partial x}-Q \frac{\partial z}{\partial y}+R\right)dA$

This gives us

$\int \int (2xy\sin(8y)+4xy^2(8x\cos(8y))-2y(x\sin(8y)))dA$
okay, so I integrate

$\int_0^{pi/16} \int_0^{pi/16} (2xy\sin(8y)+4xy^2(8x\cos(8y))-2y(x\sin(8y)))dxdy$

with x = 0 to pi/16 and y = 0 to pi/16

and keep getting:

7.37119946071407E-05

I was wondering if I am using the right limits: