84 a. Find the Jacobian of the transformation x = 4u, y = 2uv and sketch the region G: 4 ≤4u ≤ 8, 2≤2uv≤ 4, in the uv-plane. S S = ² 4 2 ›fff(x,y) R b. Then use x,y) dx dy= a. The Jacobian is fff(g( G f(g(u,v),h(u,v)) J(u,v) du dv to transform the integral dy dx into an integral over G, and evaluate both integrals. C...

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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a. Find the Jacobian of the transformation x = 4u, y = 2uv and sketch the region G: 4 ≤4u≤8, 2≤2uv ≤4, in the uv-plane.
8 4
b. Then use
f(x,y) dx dy = ¶¶f(g(u,v),h(u,v)|J(u,v)| du dv to transform the integral
R
a. The Jacobian is
G
X
4 2
dy dx into an integral over G, and evaluate both integrals.
Transcribed Image Text:a. Find the Jacobian of the transformation x = 4u, y = 2uv and sketch the region G: 4 ≤4u≤8, 2≤2uv ≤4, in the uv-plane. 8 4 b. Then use f(x,y) dx dy = ¶¶f(g(u,v),h(u,v)|J(u,v)| du dv to transform the integral R a. The Jacobian is G X 4 2 dy dx into an integral over G, and evaluate both integrals.
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