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Double integral

Please see the attached file for full problem description.

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Use a transformation to evaluate the double integral of f(x,y) given by

f(x,y)=cos(2x+y)sin(x-2y).

over the square region with vertices at (0,0) P(1,-2) Q(3,-1) & R(2,1) (My notes from class-uses substitution, change of variables)

Solution. Letting . Then . We know the equations for OP,OR,PQ and RQ are

OP: 2x+y=0;
OR:x-2y=0;
PQ:x-2y=5;
RQ:2x+y=5.

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