Find the flux of F=(3x,2y,z) through the volume bound by the xy plane, the elliptic cylinder (x/3)^2+(y/2)^2=1, and the paraboloid x^2 + y^2 =z, and hence find the components of the flux through the 3 individual surfaces.
I parametrised the whole thing with x=3rsin and y=2rcos (J=6r)
and by divergence theorem found the total flux to be 117pi
When I try to calculate the flux through the elliptic cylinder by the regular method,
with parametrisation (3cos, 2sin, z)
and the corresponding cross product (2cos, 3sin, 0)
and boundary for z is z=9-5sin^2 by plugging in the 2 equations
I get 202.5pi, which is greater than the total 117pi.