Let R denote the region in the xy-plane that lies in the first quadrant and is...

   

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Let R denote the region in the xy-plane that lies in the first quadrant and is bounded by the lines y = 1 - x, y = 2 - x, y = x + 1, and y = x - 1. Set u=x+y and v = y-x. (a) Solve for x and y in terms of u and v. (b) Find the Jacobian J(u, v). (c) Sketch the region R in the xy-coordinate system and its image under the above transfor- mation in the uv-coordinate system. (Two pictures!) (d) Use the above transformation to set up the integral v. Do not evaluate. R e(+1) drdy in terms of u and Let R denote the region in the xy-plane that lies in the first quadrant and is bounded by the lines y = 1 - x, y = 2 - x, y = x + 1, and y = x - 1. Set u=x+y and v = y-x. (a) Solve for x and y in terms of u and v. (b) Find the Jacobian J(u, v). (c) Sketch the region R in the xy-coordinate system and its image under the above transfor- mation in the uv-coordinate system. (Two pictures!) (d) Use the above transformation to set up the integral v. Do not evaluate. R e(+1) drdy in terms of u and