12/ Vse the divergence of the fleld FCX4,22= a (e,3yt sin liz),9zt²+]y through the Surfacé theorem to eva luate the flux , Where Sis the region x+y2zK8-x*=y² 二? F ds

Algebra & Trigonometry with Analytic Geometry
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ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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12/ Use the di vergence
theorem to eva lvate the flux
of the fleld F Cx,4,2)=
through the Surface S, here S is the
2.
region x+y?KzK8=x²-y²
2.
HoF.ds=?
S.
Transcribed Image Text:12/ Use the di vergence theorem to eva lvate the flux of the fleld F Cx,4,2)= through the Surface S, here S is the 2. region x+y?KzK8=x²-y² 2. HoF.ds=? S.
Expert Solution
Step 1

To Determine: use the divergence theorem to evaluate the flux of the field

                       sF.ds=?

Given: we 

      F(x, y, z)=<ez2,9y+sinx2z,9z+x2+9y2> 

Explanation: we have 

through the surface S,where S is the region x2+y2z8-x2-y2.

                   div.F=xez2+y5y+sinx2z+z9z+x2+9y2

                div. F=0+5+9=14

using cylindrical coordinates as x=rcosθ, y=rsinθ, z=z.

                   0θ2π   ,0r2  and r2z8-r2

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