I need to evaluate the flux integral
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:
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.