For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F and the boundary surface S . For each closed surface, assume N is the outward unit normal vector . 392. Use the divergence theorem to compute flux integral ∬ s F ⋅ d S , where F ( x , y , z ) = x + y j + z 4 k and S is a part of cone z = x 2 + y 2 beneath top plane z = 1 , oriented downward.
For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F and the boundary surface S . For each closed surface, assume N is the outward unit normal vector . 392. Use the divergence theorem to compute flux integral ∬ s F ⋅ d S , where F ( x , y , z ) = x + y j + z 4 k and S is a part of cone z = x 2 + y 2 beneath top plane z = 1 , oriented downward.
For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral
∫
s
F
⋅
n
d
S
for the given choice of F and the boundary surface S. For each closed surface, assume N is the outward unit normal vector.
392. Use the divergence theorem to compute flux integral
∬
s
F
⋅
d
S
, where
F
(
x
,
y
,
z
)
=
x
+
y
j
+
z
4
k
and S is a part of cone
z
=
x
2
+
y
2
beneath top plane
z
=
1
, oriented downward.
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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