For the following exercises, use a computer algebraicsystem (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F andthe boundary surface S . For each closed surface, assume Nis the outward unit normal vector. 382. [T ] F ( x , y , z ) = x y 2 i + y z 2 j + x 2 z k ; S is the surface bounded above by sphere ρ = 2 and below by cone φ = π 4 in spherical coordinates. (Think of S as thesurface of an “ice cream cone”)
For the following exercises, use a computer algebraicsystem (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F andthe boundary surface S . For each closed surface, assume Nis the outward unit normal vector. 382. [T ] F ( x , y , z ) = x y 2 i + y z 2 j + x 2 z k ; S is the surface bounded above by sphere ρ = 2 and below by cone φ = π 4 in spherical coordinates. (Think of S as thesurface of an “ice cream cone”)
For the following exercises, use a computer algebraicsystem (CAS) and the divergence theorem to evaluate surface integral
∫
s
F
⋅
n
d
S
for the given choice of F andthe boundary surface S. For each closed surface, assume Nis the outward unit normal vector.
382. [T]
F
(
x
,
y
,
z
)
=
x
y
2
i
+
y
z
2
j
+
x
2
z
k
; S is the surface bounded above by sphere
ρ
=
2
and below by cone
φ
=
π
4
in spherical coordinates. (Think of S as thesurface of an “ice cream cone”)
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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