For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 341. [T] Use a CAS and Stokes’ theorem to evaluate ∬ s c u r l F ⋅ d S , where F ( x , y , z ) = ( sin ( y + z ) − y x 2 − y 3 3 ) i + x cos ( y + z ) j + cos ( 2 y ) k and S consists of the top and the four sides but not the bottom of the cube with vertices ( ± 1 , ± 1 , ± 1 ) , oriented outward.
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 341. [T] Use a CAS and Stokes’ theorem to evaluate ∬ s c u r l F ⋅ d S , where F ( x , y , z ) = ( sin ( y + z ) − y x 2 − y 3 3 ) i + x cos ( y + z ) j + cos ( 2 y ) k and S consists of the top and the four sides but not the bottom of the cube with vertices ( ± 1 , ± 1 , ± 1 ) , oriented outward.
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
341. [T] Use a CAS and Stokes’ theorem to evaluate
∬
s
c
u
r
l
F
⋅
d
S
, where
F
(
x
,
y
,
z
)
=
(
sin
(
y
+
z
)
−
y
x
2
−
y
3
3
)
i
+
x
cos
(
y
+
z
)
j
+
cos
(
2
y
)
k
and S consists of the top and the four sides but not the bottom of the cube with vertices
(
±
1
,
±
1
,
±
1
)
, oriented outward.
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.
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
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