Miscellaneous surface integrals Evaluate the following integrals using the method of your choice. Assume normal vectors point either outward or upward . 51. ∬ S | r | d S , where S is the cylinder x 2 + y 2 = 4, for 0 ≤ z ≤ 8, and where r = 〈 x , y , z 〉
Miscellaneous surface integrals Evaluate the following integrals using the method of your choice. Assume normal vectors point either outward or upward . 51. ∬ S | r | d S , where S is the cylinder x 2 + y 2 = 4, for 0 ≤ z ≤ 8, and where r = 〈 x , y , z 〉
Miscellaneous surface integralsEvaluate the following integrals using the method of your choice. Assume normal vectors point either outward or upward.
51.
∬
S
|
r
|
d
S
, where S is the cylinder x2 + y2 = 4, for 0 ≤ z ≤ 8, and where r = 〈x, y, z〉
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.
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
Determine the coordinates of the centroid of the shaded area in millimeters.
y
2 mm
у 3 (0.3 х* - 2.4 х) mm
X =
mm
mm
I| ||
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.