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Use the transformation in Exercise 1 to evaluate the integral

$$\iint_{R}\left(2 x^{2}-x y-y^{2}\right) d x d y$$

for the region $R$ in the first quadrant bounded by the lines $y=-2 x+4, y=-2 x+7, y=x-2,$ and $y=x+1$

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University of Illinois at Urbana-Champaign