Question
Asked Nov 19, 2019
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Find the volume of the solid bound by the surface z=(2x-y)^2+(x-y-1)^2 and the plane z=4.

Question: Why do we need to use the change of variables in this equation? How do we know when to use the change of variables?

V= xty-)
=2X-y
Use
change of Variables
SS
(2x-y (Xty-4
-11
S4-
d
3
use polen; u-rnao
Vrmhg
2 2
(4r rde
Gr-r>)dr
21T
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V= xty-) =2X-y Use change of Variables SS (2x-y (Xty-4 -11 S4- d 3 use polen; u-rnao Vrmhg 2 2 (4r rde Gr-r>)dr 21T

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Expert Answer

Step 1

Given that a solid is bounded by the surface and plane.

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z (2x - y x -y- 1)2 and the plane z 4.

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Step 2

To determine th...

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The volume thus will be the difference between the two surfaces, i.e 4 - (2х — у)? + (х - у — 1)? dA V In order to make use of this formula first determine the function that we should be integrating and the region that it is to be integrating over 4 — (2х — у)? + (х — у — 1)? dA V = (2x - y)2 (x -y - 1) 4

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Calculus

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