Given that σ is the part of the surface z = 2 − y in the first octant from x = 0 to x = 1. If ψ(x, y, z) = xyz, F(x, y, z) = z i + y j + x k and n is the unit normal vector to the surface pointing outwards, evaluate the following surface integrals: (i) ZZ σ ψ(x, y, z) dS (ii) ZZ σ F . n dS

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Given that σ is the part of the surface z = 2 − y in the first octant from x = 0 to x = 1. If
ψ(x, y, z) = xyz, F(x, y, z) = z i + y j + x k and n is the unit normal vector to the surface
pointing outwards, evaluate the following surface integrals:
(i) ZZ
σ
ψ(x, y, z) dS

(ii) ZZ
σ
F . n dS

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