Hi, am kinda having trouble figuring out the following problem? any help would be highly appreciated...
Evaluate if and the surface S is given by for . (Take S to have upward orientation.)
if $\displaystyle \vec F(x,y,z)=P \vec i +Q \vec j + R \vec k$ and $\displaystyle z=g(x,y)$ then
$\displaystyle \iint_S \vec F \cdot d\vec S=\iint_D\left( -P \frac{\partial z}{\partial x}-Q \frac{\partial z}{\partial y}+R\right)dA$
This gives us
$\displaystyle \int \int (2xy\sin(8y)+4xy^2(8x\cos(8y))-2y(x\sin(8y)))dA$