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 . 383. [T] F ( x , y , z ) = x 3 i + y 3 j + 3 a 2 z k ( constant a > 0 ) ; S is the surface bounded by cylinder x 2 + y 2 = a 2 and planes z = 0 and z = 1 .
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 . 383. [T] F ( x , y , z ) = x 3 i + y 3 j + 3 a 2 z k ( constant a > 0 ) ; S is the surface bounded by cylinder x 2 + y 2 = a 2 and planes z = 0 and z = 1 .
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.
383. [T]
F
(
x
,
y
,
z
)
=
x
3
i
+
y
3
j
+
3
a
2
z
k
(
constant a
>
0
)
; S is the surface bounded by cylinder
x
2
+
y
2
=
a
2
and planes
z
=
0
and
z
=
1
.
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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