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a. Find the Jacobian of the transformation x = 4u, y= uv and sketch the region G: 4 ≤4u ≤ 8, 1 suv ≤2, in the uv-plane. 8 2 b. Then use • SS₁(x,y) dx dy = SS₁ R G a. The Jacobian is. Av Choose the correct sketch of the region G below. O A. ✔ The integral is f(g(u,v),h(u,v))|J(u,v)| du dv to transform the integral b. Write the integral over G. !! S S dvdu. Evaluate the integrals. The evaluation for both integrals is OB. Av 12- SS=0 4 1 (Type an exact answer.) dy dx into an integral over G, and evaluate both integrals. C O C. HI O D. u Q Q G

a. Find the Jacobian of the transformation x = 4u, y= uv and sketch the region G: 4 ≤4u ≤ 8, 1 suv ≤2, in the uv-plane. 8 2 b. Then use • SS₁(x,y) dx dy = SS₁ R G a. The Jacobian is. Av Choose the correct sketch of the region G below. O A. ✔ The integral is f(g(u,v),h(u,v))|J(u,v)| du dv to transform the integral b. Write the integral over G. !! S S dvdu. Evaluate the integrals. The evaluation for both integrals is OB. Av 12- SS=0 4 1 (Type an exact answer.) dy dx into an integral over G, and evaluate both integrals. C O C. HI O D. u Q Q G

Advanced Engineering Mathematics
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 = 4u, y = uv and sketch the region G: 4≤4u≤8, 1 ≤ uv≤2, in the uv-plane. 82 b. Then use a. The Jacobian is Choose the correct sketch of the region G below. O A. ft [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. R G V u Q The integral is G b. Write the integral over G. lis S S □ dv du. O B. 12 AV Evaluate the integrals. The evaluation for both integrals is. (Type an exact answer.) 4 1 O C. Q O D. Q
Transcribed Image Text:a. Find the Jacobian of the transformation x = 4u, y = uv and sketch the region G: 4≤4u≤8, 1 ≤ uv≤2, in the uv-plane. 82 b. Then use a. The Jacobian is Choose the correct sketch of the region G below. O A. ft [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. R G V u Q The integral is G b. Write the integral over G. lis S S □ dv du. O B. 12 AV Evaluate the integrals. The evaluation for both integrals is. (Type an exact answer.) 4 1 O C. Q O D. Q
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