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.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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