Hi,

I need to evaluate the flux integral $\displaystyle \iint F \cdot \hat{n}dS$

for portion of a plane x +2y+3z = 6 in the first octant and vector field F= < xy, -x^2, (x+z) >

How do i go about doing this?

I started of by doing it through parametrising the surface with r(s,t) = (3s,3t,(2-2t-s))

With normal vector equalling cross product of tangents N= (3,-6,9)

Then my bounds for integration were:

$\displaystyle 0\leqslant s \leqslant 6-2t , 0\leqslant t \leqslant 6$

then i proceeded to integrate but it became really messy and did not seem right!

so firstly, do i need to do it by parametrising the surface? secondly, are my bounds for integration correct? and lastly, It doesnt look like my normal vector is point in the right direction.