# Double integral

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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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The solution uses a transformation to evaluate the double integral.

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Please see the attached file for the full solution.

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 O(0,0) P(1,-2) Q(3,-1) & R(2,1) (My notes ...

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