The plane is perpendicular to the cylinder so you should get the full range of the cylinder cross section (0 to 2pi).
I require i little bit of help. Please see below in green text to see my issue.thanks.
use the divergence theorem to find the outward flux of F=12yi+xyj-2zk across the boundary of the region D;the region inside the solid cylinder x^2+y^2≤4 between the plane z=0 and the paraboloid
for this question i Used ..∫∫∫divFdv
According to the solutions for this question
θ varies from 0 to 2pi..
if z=0 there would only be half the cylinder..and hence half of 2pi=pi
Please explain why this is so??