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 . 386. Use the divergence theorem to calculate surface integral ∬ s F ⋅ d S , where F ( x , y , z ) = x 4 i − x 3 z 2 j + 4 x y 2 z k and S is the surface bounded by cylinder x 2 + y 2 = 1 and planes z = x + 2 and z = 0 .
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 . 386. Use the divergence theorem to calculate surface integral ∬ s F ⋅ d S , where F ( x , y , z ) = x 4 i − x 3 z 2 j + 4 x y 2 z k and S is the surface bounded by cylinder x 2 + y 2 = 1 and planes z = x + 2 and z = 0 .
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.
386. Use the divergence theorem to calculate surface integral
∬
s
F
⋅
d
S
, where
F
(
x
,
y
,
z
)
=
x
4
i
−
x
3
z
2
j
+
4
x
y
2
z
k
and S is the surface bounded by cylinder
x
2
+
y
2
=
1
and planes
z
=
x
+
2
and
z
=
0
.
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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