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Asked Dec 7, 2019
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I need help with part b

a. Find the Jacobian of the transformation x = u, y = uv and sketch the region G: 1<u<2, 1<uv<2, in the uv-plane.
2
2
f(x,y) dx dy =
| f(g(u,v),h(u,v))|J(u,v)| du dv to transform the integral
b. Then use
dy dx into an integral over G, and evaluate both integrals.
1
G
>| >
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a. Find the Jacobian of the transformation x = u, y = uv and sketch the region G: 1<u<2, 1<uv<2, in the uv-plane. 2 2 f(x,y) dx dy = | f(g(u,v),h(u,v))|J(u,v)| du dv to transform the integral b. Then use dy dx into an integral over G, and evaluate both integrals. 1 G >| >

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Expert Answer

Step 1

Given transformation is,

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y = uv and the region is, 1sus 2, 1suvs 2 Also given, jS(x,y) decdy = [[ f[g(u,v), h(u,v)J (1,1)] dudv (1)

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Step 2

The Jacobian is given by,

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|ди ду J = ây ôy | аи ду Since, :1 ди ây ây =v and ôu 3 1xи-vх0 3D и J = и

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Step 3

Jacobian J of the given tra...

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J = u

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