In the following exercises, the function f and region E are given. a. Express the region E and function f cylindrical coordinates. b. Convert the integral ∭ B f ( x , y , z ) d V into cylindrical coordinates and evaluate it. 279. E = { ( x , y , z ) | x 2 + y 2 + z 2 − 2 z ≤ 0 , x 2 + y 2 ≤ z }
In the following exercises, the function f and region E are given. a. Express the region E and function f cylindrical coordinates. b. Convert the integral ∭ B f ( x , y , z ) d V into cylindrical coordinates and evaluate it. 279. E = { ( x , y , z ) | x 2 + y 2 + z 2 − 2 z ≤ 0 , x 2 + y 2 ≤ z }
In the following exercises, the function f and region E are given.
a. Express the region E and function f cylindrical coordinates.
b. Convert the integral
∭
B
f
(
x
,
y
,
z
)
d
V
into cylindrical coordinates and evaluate it.
279.
E
=
{
(
x
,
y
,
z
)
|
x
2
+
y
2
+
z
2
−
2
z
≤
0
,
x
2
+
y
2
≤
z
}
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.
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.
3. Find the coordinates of the centroid of the triangle enclosed by x = 1, y = 0,and y = 4x.
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