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 . 390. Use the divergence theorem to compute the value ∬ s F ⋅ d S , where F ( x , y , z ) = ( y 3 + 3 x ) i + ( x z + y ) j + [ z + x 4 cos ( x 2 y ) ] k and S is the area of the region bounded by x 2 + y 2 = 1 , x ≥ 0 , y ≥ 0 , and 0 ≤ 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 . 390. Use the divergence theorem to compute the value ∬ s F ⋅ d S , where F ( x , y , z ) = ( y 3 + 3 x ) i + ( x z + y ) j + [ z + x 4 cos ( x 2 y ) ] k and S is the area of the region bounded by x 2 + y 2 = 1 , x ≥ 0 , y ≥ 0 , and 0 ≤ 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.
390. Use the divergence theorem to compute the value
∬
s
F
⋅
d
S
, where
F
(
x
,
y
,
z
)
=
(
y
3
+
3
x
)
i
+
(
x
z
+
y
)
j
+
[
z
+
x
4
cos
(
x
2
y
)
]
k
and S is the area of the region bounded by
x
2
+
y
2
=
1
,
x
≥
0
,
y
≥
0
, and
0
≤
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.
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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