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3(x + y) cos (x2 - y?) da, where R is the rectangle enclosed by the lines x - y = 0, x – y = 6, x + y = 0, and x + y = 6 Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped to R in the xy-plane; what is the Jacobian of x,y with y.v?

3(x + y) cos (x2 - y?) da, where R is the rectangle enclosed by the lines x - y = 0, x – y = 6, x + y = 0, and x + y = 6 Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped to R in the xy-plane; what is the Jacobian of x,y with y.v?

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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Evaluate the integral by making an appropriate change of variables. 3(x + v) cos (x2 - v2) dA, where R is the rectangle enclosed by the lines x - y = 0, x – y = 6, x + y = 0, and x + y = 6 Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped to R in the xy-plane; what is the Jacobian of x,y with respect to u,v?
Transcribed Image Text:Evaluate the integral by making an appropriate change of variables. 3(x + v) cos (x2 - v2) dA, where R is the rectangle enclosed by the lines x - y = 0, x – y = 6, x + y = 0, and x + y = 6 Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped to R in the xy-plane; what is the Jacobian of x,y with respect to u,v?
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