a. Find the Jacobian of the transformation x=u, y=3uv and sketch the region G: 1 su≤2, 3≤ 3uv ≤6, in the uv-plane. 26 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. a. The Jacobian is Choose the correct sketch of the region G below. O A. b. Write the integral over G. The integral is dv du. Evaluate the integrals. The evaluation for both integrals is B. (Type an exact answer.) C. 1 3 Q D.

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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a. Find the Jacobian of the transformation x = u, y = 3uv and sketch the region G: 1 ≤u≤2, 3 ≤3uv ≤ 6, in the uv-plane.
26
b. Then use
afff(x,y) dx dy = f(g
R
evaluate both integrals.
V
a. The Jacobian is
Choose the correct sketch of the region G below.
O A.
u
The integral is
dy = f(g(u,v),h(u,v)|J(u,v)| du dv to transform the integral
Q
b. Write the integral over G.
-II-
dv du.
B.
Evaluate the integrals.
The evaluation for both integrals is. (Type an exact answer.)
u
1 3
dy dx into an integral over G, and
X
D.
Q
✔
Transcribed Image Text:a. Find the Jacobian of the transformation x = u, y = 3uv and sketch the region G: 1 ≤u≤2, 3 ≤3uv ≤ 6, in the uv-plane. 26 b. Then use afff(x,y) dx dy = f(g R evaluate both integrals. V a. The Jacobian is Choose the correct sketch of the region G below. O A. u The integral is dy = f(g(u,v),h(u,v)|J(u,v)| du dv to transform the integral Q b. Write the integral over G. -II- dv du. B. Evaluate the integrals. The evaluation for both integrals is. (Type an exact answer.) u 1 3 dy dx into an integral over G, and X D. Q ✔
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