48 a. Find the Jacobian of the transformation x=2u, y=4uv and sketch the region G: 2 ≤2u≤ 4, 4s4uvs8, in the uv-plane. is st 2 4 b. Then use SS₁(x,y) R Av a. The Jacobian is Choose the correct sketch of the region G below. O A. f(x,y) dx dy= =fff(g(u,v),k f(g(u,v),h(u,v)) J(u,v) du dv to transform the integral G b. Write the integral over G. The integral is SSO dve dv du. Evaluate the integrals. The evaluation for both integrals is O B. AV 42 (Type an exact answer.) dy dx into an integral over G, and evaluate both integrals. O C. 6 AV Q O D. Q OU

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 = 2u, y = 4uv and sketch the region G: 2 ≤2u≤ 4, 4≤4uv ≤8, in the uv-plane.
4 8
y
b. Then use f(x,y) dx dy = [[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.
X
R
G
a. The Jacobian is
Choose the correct sketch of the region G below.
O A.
Av
9
Q
Q
b. Write the integral over G.
The integral is dv du.
s s
Evaluate the integrals.
The evaluation for both integrals is
OB.
AV
12
(Type an exact answer.)
24
www
O C.
AV
6
U
ON
O D.
Q
Transcribed Image Text:a. Find the Jacobian of the transformation x = 2u, y = 4uv and sketch the region G: 2 ≤2u≤ 4, 4≤4uv ≤8, in the uv-plane. 4 8 y b. Then use f(x,y) dx dy = [[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. X R G a. The Jacobian is Choose the correct sketch of the region G below. O A. Av 9 Q Q b. Write the integral over G. The integral is dv du. s s Evaluate the integrals. The evaluation for both integrals is OB. AV 12 (Type an exact answer.) 24 www O C. AV 6 U ON O D. Q
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