Final answer:
The question is about evaluating a double integral over a parallelogram using a transformation to different variables, but the full transformation is not provided. Without the complete expression for y, we can't evaluate the integral or provide a detailed process. Typically, a Jacobian and new integration bounds would be needed.
Step-by-step explanation:
The question involves using a given transformation to evaluate a double integral over a specific domain D, which in this case is defined as a parallelogram. A double integral ∬_D x*y dA requires application of a change of variables to a more standard region in the uv-plane when the variables x and y are defined as linear combinations of u and v. However, as the full transformation is not provided, the complete evaluation process cannot be detailed. Typically, one would find the Jacobian determinant of the transformation to use in converting the integral in xy-coordinates to uv-coordinates. The new bounds of integration in terms of u and v would also need to be determined by examining the mapping of the original parallelogram corners in the xy-plane to the uv-plane. After setting up the integral in uv-coordinates, the integrand would be x(u, v)*y(u, v) multiplied by the Jacobian, and then it would be integrated over the new region.