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Asked Aug 3, 2019
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How do I choose  my g(u,v) and h(u,v)?

Problem #3: Consider the double integral Jp x dA, where R is bounded by the lines
y=2x- 1, y = 2x + 1, y = 1-x, and y 3 - x.
X- 1-y
メニ
g(u, v) and y
h(u,v).
Define an
2xrl
42x-1
appropriate transformation of the form x =
a.
1-x>2x1
23
(o,)
3-x
3-x-2
2-3x
b. Find the Jacobian of your transformation.
Evaluate the integral using your transformation.
c.
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Problem #3: Consider the double integral Jp x dA, where R is bounded by the lines y=2x- 1, y = 2x + 1, y = 1-x, and y 3 - x. X- 1-y メニ g(u, v) and y h(u,v). Define an 2xrl 42x-1 appropriate transformation of the form x = a. 1-x>2x1 23 (o,) 3-x 3-x-2 2-3x b. Find the Jacobian of your transformation. Evaluate the integral using your transformation. c.

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Expert Answer

Step 1

The double integral is given by,

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|*dА, where R is bounded by the 1lines у 3 2х -1, у%3 2х +1,у%3D1-х and у%33-х

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Step 2

Now consider,

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..(1) (2) v y 2x

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Step 3

Solve the equations ...

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Subtract equations (1) and (2) у - 2х %3D v y x — 3х —D v — и х 3 3 3 in equation (1) 3 3 Substitute -- 3 3 y=-+u 3 3 2u 3 3

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