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Unformatted text preview: x 2 + 6 xy + 4 y 2 = 4. 2 6. Let D xy be the region bounded by y = 1-x , y = 2-x , y = 0 and x = y and let ( u,v ) = F ( x,y ) = ± x-y, 1 x + y ² . a) Sketch the image of D under F in the uv-plane. b) Find the Jacobian of F and show that it is never 0 on D . c) Find the mapping F-1 and the Jacobian for F-1 . d) Use the mapping F to evaluate ZZ D xy x-y x + y dA . 7. Use MAPLE to evaluate the following double integrals. (Use Maple Help to learn how to use the “int” command) a) R D xy ( x + y ) 3 dA where D xy is the triangular region with vertices (0 , 0), (1 , 1), and (2 , 0). b) R D xy y x dA where D xy is the region in the ﬁrst quadrant bounded by y = 0, y = x , and x 2 + 4 y 2 = 4....
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