Miscellaneous surface integrals Evaluate the following integrals using the method of your choice. Assume normal vectors point either outward or upward . 53. ∬ S ( x , 0 , z ) x 2 + z 2 ⋅ n d S , where S is the cylinder x 2 + z 2 = a 2 , | y | ≤ 2
Miscellaneous surface integrals Evaluate the following integrals using the method of your choice. Assume normal vectors point either outward or upward . 53. ∬ S ( x , 0 , z ) x 2 + z 2 ⋅ n d S , where S is the cylinder x 2 + z 2 = a 2 , | y | ≤ 2
Miscellaneous surface integralsEvaluate the following integrals using the method of your choice. Assume normal vectors point either outward or upward.
53.
∬
S
(
x
,
0
,
z
)
x
2
+
z
2
⋅
n
d
S
, where S is the cylinder x2 + z2 = a2,
|
y
|
≤
2
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.
Evaluate the surface integral.
J y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u sin(v), v), 0sus 6,0 SV SR.
[(10) ()-1]
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For an area A in the x-y plane, in the expression I₂ = 1x + ly, the term /₂ is the:
Minimum rectangular moment of inertia or second moment of area.
O Product of inertia.
Polar moment of inertia.
O Maximum rectangular moment of inertia or second moment of area.
Calculate ff f(x, y, z) d.S for the given surface and function.
x² + y² = 25, 0≤ z ≤ 4; f(x, y, z) = e¯²
Consider the shown work.
To =
T, =
аф
де
=
д
(5 cos 0, 5 sin 0, z) = (-5 sin 0, 5 cos 0, 0)
do
d
-(5 cos 0, 5 sin 0, z) = (0,0,1)
дz
i
N(0, z) = T₁ × T₂ = -5 sin 0
0
||N(0, z)|| =
5 cos 0
0
2π 4
[[ f(x, y, 2) ds = [²* ["^ e
S
(5 cos 0)² + (5 sin 0)² + 0 =
e² do dz
k
0 = (5 cos 0)i + (5 sin 0)j =
1
Identify the first error in the work shown.
/25 (cos² 0 + sin²0)
The surface integral is written incorrectly.
No errors exist in the work shown.
The parametrization of the cylinder is incorrect.
The normal vector N(0, z) is incorrect.
(5 cos 0, 5 sin 0, 0)
√25 = 5
Thomas' Calculus: Early Transcendentals (14th Edition)
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