Let W be the region bounded by planes $$x=0, y=0, y=3, x+2z=6$$ Evaluate the surface integral using Gauss Divergence theorem where F= $$ 2xy \hat i + yz^2 \hat j + xz \hat k$$
I am able to set bounds correctly- x: 0 to 6, y: 0 to 3, z: 0 to $$\frac{6-x}{2}$$
The divergence of F is $$2y + z^2 + x$$
hence, by Gauss divergence theorem,
$$\int_0^{6}\int_0^{\frac{6-x}{2}}\int_0^{3} (2y+z^{2}+x)dydzdx$$
But I am making some mistakes during evaluation of integral which is messing up the answer. Please help.