Average Value In Exercises 63-66, find the average value of the function over the given solid region. The average value of a continuous function f(x, y, z) over a solid region is Average value = 1 V ∭ Q f ( x , y , z ) d V where V is the volume of the solid region Q. f ( x , y , z ) = x + y over die solid bounded by the sphere x 2 + y 2 + z 2 = 3
Average Value In Exercises 63-66, find the average value of the function over the given solid region. The average value of a continuous function f(x, y, z) over a solid region is Average value = 1 V ∭ Q f ( x , y , z ) d V where V is the volume of the solid region Q. f ( x , y , z ) = x + y over die solid bounded by the sphere x 2 + y 2 + z 2 = 3
Solution Summary: The author calculates the average value of the function f(x,y,z)=x+y over the solid region Q.
Average Value In Exercises 63-66, find the average value of the function over the given solid region. The average value of a continuous function f(x, y, z) over a solid region is
Average
value
=
1
V
∭
Q
f
(
x
,
y
,
z
)
d
V
where V is the volume of the solid region Q.
f
(
x
,
y
,
z
)
=
x
+
y
over die solid bounded by the sphere
x
2
+
y
2
+
z
2
=
3
Z =
(a) What is the equation of the plane passing through the points (2, 0, 0), (0, 2, 0), and (0, 0, 1)?
(b) Find the volume of the region bounded by this plane and the planes x = : 0, y = 0, and z = 0.
volume =
Average value Find the average value of ƒ(x, y, z) =30xz √x2 + y over the rectangular solid in the first octant boundedby the coordinate planes and the planes x = 1, y = 3, z = 1.
IntegrationDetermine the volume of the solid below the paraboloid z=x²+3y² and above the region bounded by the planes x=0 ,y=1,y=x and z=0
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