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”)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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