a. Find the Jacobian of the transformation x=2u, y=2uv and sketch the region G: 2≤2u≤6, 2≤2uv≤6, in the uv-plane. 6 6 b. Then use se dy=[fratuv) ·SS₁x f(x,y) dx dy = R 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. X 22

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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a. Find the Jacobian of the transformation x = 2u, y = 2uv and sketch the region G: 2≤2u ≤6, 2≤2uv ≤ 6, in the uv-plane.
6 6
b. Then use
SS¶‹›
R
f(x,y) dx dy = SS
SS
G
a. The Jacobian is
AV
Choose the correct sketch of the region G below.
O A.
▬▬▬▬▬
f(g(u, v),
,.v),.h(u,v))|J(u,v)| du dv to transform the integral dy dx into an integral over G, and evaluate both integrals.
u
b. Write the integral over G.
The integral is dv du.
II
Evaluate the integrals.
The evaluation for both integrals is
O B.
AV
13-
(Type an exact answer.)
2
C.
-11
u
✓
✔
O D.
AV
u
Transcribed Image Text:a. Find the Jacobian of the transformation x = 2u, y = 2uv and sketch the region G: 2≤2u ≤6, 2≤2uv ≤ 6, in the uv-plane. 6 6 b. Then use SS¶‹› R f(x,y) dx dy = SS SS G a. The Jacobian is AV Choose the correct sketch of the region G below. O A. ▬▬▬▬▬ f(g(u, v), ,.v),.h(u,v))|J(u,v)| du dv to transform the integral dy dx into an integral over G, and evaluate both integrals. u b. Write the integral over G. The integral is dv du. II Evaluate the integrals. The evaluation for both integrals is O B. AV 13- (Type an exact answer.) 2 C. -11 u ✓ ✔ O D. AV u
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