For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 358. [T] Use a CAS and let F ( x , y , z ) = x y 2 i + ( y z − x ) j + e y x z k . Use Stokes’ theorem to compute the surface integral of curl F over surface S with inward orientation consisting of cube [ 0 , 1 ] × [ 0 , 1 ] × [ 0 , 1 ] with the right side missing.
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 358. [T] Use a CAS and let F ( x , y , z ) = x y 2 i + ( y z − x ) j + e y x z k . Use Stokes’ theorem to compute the surface integral of curl F over surface S with inward orientation consisting of cube [ 0 , 1 ] × [ 0 , 1 ] × [ 0 , 1 ] with the right side missing.
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
358. [T] Use a CAS and let
F
(
x
,
y
,
z
)
=
x
y
2
i
+
(
y
z
−
x
)
j
+
e
y
x
z
k
. Use Stokes’ theorem to compute the surface integral of curl F over surface S with inward orientation consisting of cube
[
0
,
1
]
×
[
0
,
1
]
×
[
0
,
1
]
with the right side missing.
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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