Final answer:
To solve the given integral via a change of variables, we need the full transformation for both 'x' and 'y', as well as the limits of integration. We then calculate the Jacobian determinant for the transformation and substitute into the integral before integrating with respect to the new variables.
Step-by-step explanation:
To solve the integral (x - 2y^2) / -3 da using a change of variables where x = 2uv, we need to express the differential area 'da' in terms of the new variables 'u' and 'v'. First, we should find the Jacobian determinant of the transformation to correctly change the variables. Once we have the Jacobian, we substitute it along with the new expression for 'x' into the integral and integrate with respect to the new variables 'u' and 'v'. However, without additional information such as the other part of transformation for 'y' and the limits of integration, we cannot proceed further. It is essential to know the full change of variable formulas and the new limits of integration to complete this problem.