Use the divergence theorem to find the outward flux    ∫     ∫ SF · n dS   of the vector field F  =  tan−1(9y + 4z) i  +  e z2 + 6 cos x j  +   √ x2 + y2 + z2 k,  where S is the surface of the region bounded by the graphs of  z  =   √ x2 + y2  and  x2 + y2 + z2  =  16.

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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Use the divergence theorem to find the outward flux 
 
 
 
S
F·ndS   of the vector field F  =  tan−1(9y + 4z) i  +  ez2 + 6 cos xj  +  
x2 + y2 + z2
 k,  where S is the surface of the region bounded by the graphs of  z  =  
x2 + y2
  and  x2 + y2 + z2  =  16.
Problem #5:
Use the divergence theorem to find the outward flux || F.n dS
of
the
vector
field
tan(9y + 42) i + ez +6 cos x j + Vx2 + v2 + =2 k, where S is
the surface of the region bounded by the graphs of : =
and x? + y2 + =?
F
+y
16.
Enter your answer symbolically,
as in these examples
Problem #5:
Transcribed Image Text:Problem #5: Use the divergence theorem to find the outward flux || F.n dS of the vector field tan(9y + 42) i + ez +6 cos x j + Vx2 + v2 + =2 k, where S is the surface of the region bounded by the graphs of : = and x? + y2 + =? F +y 16. Enter your answer symbolically, as in these examples Problem #5:
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