a. Find the Jacobian of the transformation x=u, y = uv and sketch the region G: 1 sus3, 1 suvs 3, in the uv-plane. 33 b. Then use fff(x,y) dx dy = f(g(u.v)h(uv)) J(u.v) du dv to transform the integral dy dx into an integral over G, and evaluate both integrals. R G a. The Jacobian is Choose the correct sketch of the region G below. O A. Av Q b. Write the integral over G. The integral is dv du. -??- Evaluate the integrals. The evaluation for both integrals is. (Type an exact answer.) OB. 11 Q O C. FFFHH! Q O D. H Q
a. Find the Jacobian of the transformation x=u, y = uv and sketch the region G: 1 sus3, 1 suvs 3, in the uv-plane. 33 b. Then use fff(x,y) dx dy = f(g(u.v)h(uv)) J(u.v) du dv to transform the integral dy dx into an integral over G, and evaluate both integrals. R G a. The Jacobian is Choose the correct sketch of the region G below. O A. Av Q b. Write the integral over G. The integral is dv du. -??- Evaluate the integrals. The evaluation for both integrals is. (Type an exact answer.) OB. 11 Q O C. FFFHH! Q O D. H Q
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:a. Find the Jacobian of the transformation x = u, y = uv and sketch the region G: 1 ≤u≤3, 1 ≤uv ≤ 3, in the uv-plane.
3 3
b. Then use
e Sf(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.
Q
b. Write the integral over G.
The integral is
dv du.
Evaluate the integrals.
The evaluation for both integrals is. (Type an exact answer.)
O B.
1 1
C
O C.
H
Q
O D.
Q
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