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Use the transformation in Exercise 3 to evaluate the integral

$$\iint_{R}\left(3 x^{2}+14 x y+8 y^{2}\right) d x d y$$

for the region $R$ in the first quadrant bounded by the lines $y=-(3 / 2) x+1, y=-(3 / 2) x+3, y=-(1 / 4) x, \quad$ and $\quad y=$ $-(1 / 4) x+1 .$

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Missouri State University

Harvey Mudd College

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Boston College

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University of Illinois at Urbana-Champaign