Module 17 : Surfaces, Surface Area, Surface integrals, Divergence Theorem and applications
Lecture 50 : Application of surface integrals [Section 50.2]
 

outward across the portion of the cone that lies above the -plane. The surface is given by . Thus, the normal vector is

Note that for the outward normal, the component is always positive. So, we choose

for Hence,

(ii)
Let us compute the flux of the vector field
 

across parabolic cylinder given by

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