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Let S be the region bounded by y − x = −4, y−x = 0, 3 y+x = 4 and 3y+x = 12. Use a linear transformation to transform S into a rectangular region and evaluate the integral ∬S20(y − x)2(3y + x) dAxy (It may help to sketch the region on the uv-axis)

Let S be the region bounded by y − x = −4, y−x = 0, 3 y+x = 4 and 3y+x = 12. Use a linear transformation to transform S into a rectangular region and evaluate the integral ∬S20(y − x)2(3y + x) dAxy (It may help to sketch the region on the uv-axis)

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  1. (12 points) Let S be the region bounded by y − x = − 4 , y − x = 0 , 3 y + x = 4 and 3 y + x = 12 . Use a linear transformation to transform S into a rectangular region and evaluate the integral
∬ S 20 ( y − x ) 2 ( 3 y + x ) d A x y
(It may help to sketch the region on the u v -axis)

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