The region E between the paraboloid z = 1 - 2² - y² and the plane z = 0 is shown in the 3D model below. To find the average value of the function f(x, y, z) = z²z+ y²z on this region, first calculate the volume V(E) of the region using polar coordinates: V(E)= Switch to polar coordinates to integrate f over the region and get the average value: fave 15 x N 1.5 -0.5
The region E between the paraboloid z = 1 - 2² - y² and the plane z = 0 is shown in the 3D model below. To find the average value of the function f(x, y, z) = z²z+ y²z on this region, first calculate the volume V(E) of the region using polar coordinates: V(E)= Switch to polar coordinates to integrate f over the region and get the average value: fave 15 x N 1.5 -0.5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The region E between the paraboloid z = 1 - 2² - y² and the plane z = 0 is shown in the 3D model
below.
To find the average value of the function f(x, y, z) = x²z+ y²z on this region, first calculate the volume
V(E) of the region using polar coordinates:
V(E)
Switch to polar coordinates to integrate f over the region and get the average value:
fave =
1.5
N
1.5
-0.5
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